## 金融代写|量化风险管理代写Quantitative Risk Management代考|PROJMGNT1002

statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risks faced by a financial firm

Decrease in the value of the investments on the asset side of the balance sheet (e.g. losses from securities trading or credit risk).

• Maturity mismatch (large parts of the assets are relatively illiquid (longterm) whereas large parts of the liabilities are rather short-term obligations. This can lead to a default of a solvent bank or a bank run).
• The prime risk for an insurer is insolvency (risk that claims of policy holders cannot be met). On the asset side, risks are similar to those of a bank. On the liability side, the main risk is that reserves are insufficient
• to cover future claim payments. Note that the liabilities of a life insurer are of a long-term nature and subject to multiple categories of risk (e.g. interest rate risk, inflation risk and longevity risk).
• So risk is found on both sides of the balance sheet and thus RM should not focus on the asset side alone.
• There are different notions of capital. One distinguishes:
Equity capital $\quad-$ Value of assets – debt;
• Measures the firm’s value to its shareholders;
• Can be split into shareholder capital (initial capital invested in the firm) and retained earnings (accumulated earnings not paid to shareholders).
Regulatory capital – Capital required according to regulatory rules;
• For European insurance firms: Minimum (MCR) and solvency capital requirements (SCR);
• A regulatory framework also specifies the capital quality. One distinguishes Tier 1 capital (i.e. shareholder capital + retained earnings; can act in full as buffer) and Tier 2 capital (includes other positions on the balance sheet).
• Capital required to control the probability of becoming insolvent (typically over one year);
• Internal assessment of risk capital;
• Aims at a holistic view (assets and liabilities) and works with fair values of balance sheet items.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Modelling value and value change

We set up a general mathematical model for (changes in) value caused by financial risks. To this end we work on a probability space $(\Omega, \mathcal{F}, \mathbb{P})$ and consider a risk or loss as a random variable $X: \Omega \rightarrow \mathbb{R}($ or: $L$ ).

• Consider a portfolio of assets and possibly liabilities. The value of the portfolio at time $t$ (today) is denoted by $V_t$ (a random variable; assumed to be known at $t$; its $d f$ is typically not trivial to determine!).
• We consider a given time horizon $\Delta t$ and assume:
1) the portfolio composition remains fixed over $\Delta t$;
2) there are no intermediate payments during $\Delta t$
$\Rightarrow$ Fine for small $\Delta t$ but unlikely to hold for large $\Delta t$.
• The change in value of the portfolio is given by
$$\Delta V_{t+1}=V_{t+1}-V_t$$
and we define the (random) loss by the sign-adjusted value change
$$L_{t+1}=-\Delta V_{t+1}$$
(as QRM is mainly concerned with losses).

1) The distribution of $L_{t+1}$ is called loss distribution.
2) Practitioners often consider the profit-and-loss $(P \& L)$ distribution which is the distribution of $-L_{t+1}=\Delta V_{t+1}$.
3) For longer time intervals, $\Delta V_{t+1}=V_{t+1} /(1+r)-V_t$ ( $r=$ risk-free interest rate) would be more appropriate, but we will mostly neglect this issue.

• $V_t$ is typically modelled as a function $f$ of time $t$ and a $d$-dimensional random vector $\boldsymbol{Z}=\left(Z_{t, 1}, \ldots, Z_{t, d}\right)$ of risk factors, that is,
$$V_t=f\left(t, \boldsymbol{Z}t\right) \quad \text { (mapping of risks) }$$ for some measurable $f: \mathbb{R}{+} \times \mathbb{R}^d \rightarrow \mathbb{R}$. The choice of $f$ and $\boldsymbol{Z}_t$ is problem-specific (typically known, but possibly difficult to evaluate).
• It is often convenient to work with the risk-factor changes
$$\boldsymbol{X}{t+1}=\boldsymbol{Z}{t+1}-\boldsymbol{Z}t .$$ We can rewrite $L{t+1}$ in terms of $\boldsymbol{X}{t+1}$ via \begin{aligned} L{t+1} & =-\left(V_{t+1}-V_t\right)=-\left(f\left(t+1, \boldsymbol{Z}{t+1}\right)-f\left(t, \boldsymbol{Z}_t\right)\right) \ & =-\left(f\left(t+1, \boldsymbol{Z}_t+\boldsymbol{X}{t+1}\right)-f\left(t, \boldsymbol{Z}t\right)\right) \end{aligned} We see that the loss $d f$ is determined by the loss df of $X{t+1}$. We will thus also write $L_{t+1}=L\left(\boldsymbol{X}_{t+1}\right)$, where $L(\boldsymbol{x})=-\left(f\left(t+1, \boldsymbol{Z}_t+\boldsymbol{x}\right)-f\left(t, \boldsymbol{Z}_t\right)\right)$ is known as loss operator.

# 量化风险管理代考

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risks faced by a financial firm

• 期限错配（大部分资产流动性相对较差（长期），而大部分负债是相当短期的债务。这可能导致有偿付能力的银行违约或银行挤兑）。
• 保险公司面临的主要风险是资不抵债（无法满足保单持有人索赔的风险）。在资产方面，风险类似于银行的风险。负债端，主要风险是准备金不足
• 以支付未来的理赔费用。请注意，人寿保险公司的负债具有长期性质，并受到多种风险的影响（例如利率风险、通胀风险和长寿风险）。
• 因此，资产负债表的两边都存在风险，因此 RM 不应只关注资产方面。
• 有不同的资本概念。一区分：
股权资本−资产价值——债务；
• 衡量公司对其股东的价值；
• 可以分为股东资本（投资于公司的初始资本）和留存收益（未支付给股东的累计收益）。
监管资本——监管规定要求的资本；
• 对于欧洲保险公司：最低 (MCR) 和偿付能力资本要求 (SCR)；
• 监管框架还规定了资本质量。一种区分一级资本（即股东资本+留存收益；可以完全作为缓冲）和二级资本（包括资产负债表上的其他头寸）。
• 控制破产可能性所需的资本（通常超过一年）；
• 风险资本内部评估；
• 以整体观点（资产和负债）为目标，并处理资产负债表项目的公允价值。

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Modelling value and value change

• 考虑一个资产组合，可能还有负债。投资组合当时的价值 $t$ (今天) 表示为 $V_t$ (一个随机变量; 假设 在 $t ;$ 它的 $d f$ 确定起来通常不是微不足道的））。
• 我们考虑给定的时间范围 $\Delta t$ 并假设:
1) 投资组合构成在 $\Delta t$;
2）期间没有中间付款 $\Delta t$
$\Rightarrow$ 适合小的 $\Delta t$ 但不太可能长期持有 $\Delta t$.
• 投资组合价值的变化由下式给出
$$\Delta V_{t+1}=V_{t+1}-V_t$$
我们通过符号调整后的值变化来定义 (随机) 损失
$$L_{t+1}=-\Delta V_{t+1}$$
(因为 $\mathrm{QRM}$ 主要关注损失) 。
1) 分布 $L_{t+1}$ 称为损失分布。
2) 从业者往往考虑盈亏 $(P \& L)$ 分布这是分布 $-L_{t+1}=\Delta V_{t+1}$.
3) 对于更长的时间间隔， $\Delta V_{t+1}=V_{t+1} /(1+r)-V_t(r=$ 无风险利率) 会更合适，但我们大多会 忽略这个问题。
• $V_t$ 通常被建模为一个函数 $f$ 时间的 $t$ 和一个 $d$ 维随机向量 $\boldsymbol{Z}=\left(Z_{t, 1}, \ldots, Z_{t, d}\right)$ 的风险因素，即
$$V_t=f(t, \boldsymbol{Z} t) \quad \text { (mapping of risks) }$$
对于一些可测量的 $f: \mathbb{R}+\times \mathbb{R}^d \rightarrow \mathbb{R}$. 的选择 $f$ 和 $Z_t$ 是特定于问题的（通常是已知的，但可能难 以评估）。
• 处理风险因素变化通常很方便
$$\boldsymbol{X} t+1=\boldsymbol{Z} t+1-\boldsymbol{Z} t .$$
我们可以重写 $L t+1$ 按照 $\boldsymbol{X} t+1$ 通过
$$L t+1=-\left(V_{t+1}-V_t\right)=-\left(f(t+1, \boldsymbol{Z} t+1)-f\left(t, \boldsymbol{Z}t\right)\right) \quad=-\left(f \left(t+1, \boldsymbol{Z}_t+\boldsymbol{X} t\right.\right.$$ 我们看到损失 $d f$ 由损失 df 决定 $X t+1$. 因此我们也将写 $L{t+1}=L\left(\boldsymbol{X}_{t+1}\right)$ ，在哪里$L(\boldsymbol{x})=-\left(f\left(t+1, \boldsymbol{Z}_t+\boldsymbol{x}\right)-f\left(t, \boldsymbol{Z}_t\right)\right)$ 被称为损失算子。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 金融代写|量化风险管理代写Quantitative Risk Management代考|PROJMGNT5004

statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Why manage financial risk

• Society (single customers and as a whole (systemic risk)) relies on the stability of the banking and insurance system.
• This is related to systemic importance of the company in question (size and connectivity to other firms). Considering some firms as too big to fail creates a moral hazard (should be avoided!) since the management of such a firm may take more risk knowing that it would be bailed out in a crisis.
• Better risk management can reduce the risk of company failure and protect customers and policyholders. However, regulation must be designed with care and should not promote herding, procyclical behaviour or other forms of endogenous risk that could result in a systemic crisis.
• We treat QRM as a quantitative science using the language of mathematics in general, and probability and statistics in particular.
• Probability and statistics provide us with a suitable language and with appropriate concepts for describing financial risks.
• We also point out assumptions and limitations of the methodology used.
• The $Q$ in QRM is an essential part of the RM process. We believe it remains (if applied correctly and honestly) a part of the solution to managing risk (not the problem). See also Shreve (2008):
“Don’t blame the quants. Hire good ones instead and listen to them.”

## 金融代写|量化风险管理代写Quantitative Risk Management代考|The nature of the challenge

• Our approach to QRM has two main strands:
• Put current practice onto a firmer mathematical ground;
• Put together techniques and tools which go beyond current practice and address some of the deficiencies.
• In particular, some of the challenges of QRM are:
• Extremes matter.
• Interdependence and concentration of risks.
• The problem of scale (models for all risk factors may not be feasible).
• Interdisciplinarity.
• Communication and education.

Balance sheet equation: Assets $=$ Liabilities $=$ Debt $+$ Equity. If equity $>0$, the company is solvent, otherwise insolvent.

Valuation of the items on the balance sheet is a non-trivial task.

• Amortized cost accounting values a position a book value at its inception and this is carried forward/progressively reduced over time.

Fair-value accounting values assets at prices they are sold and liabilities at prices that would have to be paid in the market. This can be challenging for non-traded or illiquid assets or liabilities.

There is a tendency in the industry to move towards fair-value accounting. Market consistent valuation in Solvency II follows similar principles.

# 量化风险管理代考

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Why manage financial risk

• 社会（单一客户和整体（系统性风险））依赖于银行和保险体系的稳定性。
• 这与相关公司的系统重要性（规模和与其他公司的联系）有关。将某些公司视为太大而不能倒闭会产生道德风险（应该避免！），因为此类公司的管理层可能会承担更多风险，因为他们知道自己会在危机中得到救助。
• 更好的风险管理可以降低公司倒闭的风险并保护客户和保单持有人。然而，监管必须谨慎设计，不应助长羊群行为、顺周期行为或其他可能导致系统性危机的内生风险形式。
• 我们将 QRM 视为一门使用一般数学语言，特别是概率和统计语言的定量科学。
• 概率和统计为我们提供了一种合适的语言和合适的概念来描述金融风险。
• 我们还指出了所用方法的假设和局限性。
• 这问在 QRM 中是 RM 过程的重要组成部分。我们相信它仍然（如果正确和诚实地应用）是管理风险（而不是问题）的解决方案的一部分。另见 Shreve (2008)：
“不要责怪宽客。相反，请聘请优秀的人并听取他们的意见。”

## 金融代写|量化风险管理代写Quantitative Risk Management代考|The nature of the challenge

• 我们的 QRM 方法有两个主要方面：
• 将当前的实践置于更坚实的数学基础上；
• 将超越当前实践的技术和工具放在一起并解决一些缺陷。
• 特别是，QRM 的一些挑战是：
• 极端很重要。
• 相互依赖和风险集中。
• 规模问题（所有风险因素的模型可能不可行）。
• 跨学科。
• 沟通和教育。

• 摊余成本会计对头寸的初始账面价值进行估值，并随着时间的推移结转/逐渐减少。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 金融代写|量化风险管理代写Quantitative Risk Management代考|FNCE90082

statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk and randomness

• The Concise Oxford English Dictionary: “hazard, a chance of bad consequences, loss or exposure to mischance”.
• McNeil, Frey, and Embrechts (2005): “any event or action that may adversely affect an organization’s ability to achieve its objectives and execute its strategies”.
• No single one-sentence definition captures all aspects of risk.
For us: risk $=$ chance of loss $\Rightarrow$ randomness

We will mostly model situations in which an investor holds today an asset with an uncertain future value.

We use probabilistic notions (random variables, random vectors, distributions, stochastic processes) and statistical tools. In particular, we assume to work on a probability space $(\Omega, \mathcal{F}, \mathbb{P})$; see Kolmogorov (1933).

There are various types of risks. We focus on (those affected by regulation):
Market risk Risk of loss in a financial position due to changes in the underlying components (e.g. stock/bond/commodity prices)
Credit risk Risk of a counterparty failing to meet its obligations (default), i.e. the risk of not receiving promised repayments (e.g. loans/bonds).
Operational risk (OpRisk) Risk of loss resulting from inadequate or failed internal processes, people and systems or from external events (e.g. fraud, fat-finger trades, earthquakes).

There are many other types of risks such as liquidity risk, underwriting risk, or model risk (the risk of using a misspecified or inappropriate model for measuring risk; model risk is always present to some degree).

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Measurement and management

• Suppose we hold a portfolio of $d$ investments with weights $w_1, \ldots, w_d$. Let $X_j$ denote the change in value of the $j$ th investment. The change in value – profit and loss $(P \& L)$ – of the portfolio over a given holding period is then
$$X=\sum_{j=1}^d w_j X_j$$
Measuring the risk now consists of determining the distribution function $F$ (or functionals of it, e.g. mean, variance, $\alpha$-quantiles $F^{\leftarrow}(\alpha)=$ $\inf {x \in \mathbb{R}: F(x) \geq \alpha})$.
• To this end, we need a properly calibrated joint model for $\boldsymbol{X}=$ $\left(X_1, \ldots, X_d\right)$. Statistical estimates of $F$ or one of its functionals are obtained based on historical observations of this model.

What is RM? Kloman (1990) writes:
“RM is a discipline for living with the possibility that future events may cause adverse effects.”
$\Rightarrow$ It is about ensuring resilience to future events.
Note that financial firms are not passive/defensive towards risk, banks and insurers actively/willingly take risks because they seek a return. RM thus belongs to their core competence.
What does managing risks involve?
Determine the capital to hold to absorb losses, both for regulatory purposes (to comply with regulators) and economic capital purposes (to survive as a company).

• Ensuring portfolios are well diversified.
• Optimizing portfolios according to risk-return considerations.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk and randomness

• 简明牛津英语词典：“hazard, a chance of bad consequences, loss or exposure to mischance”。
• McNeil、Frey 和 Embrechts（2005 年）：“任何可能对组织实现其目标和执行其战略的能力产生不利影响的事件或行动”。
• 没有一个单一的一句话定义可以涵盖风险的所有方面。
对我们来说：风险=损失的机会⇒随机性

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Measurement and management

• 假设我们持有一个投资组合 $d$ 权重投资 $w_1, \ldots, w_d$. 让 $X_j$ 表示值的变化 $j$ 第投资。价值的变化一损益 $(P \& L)$ – 在给定的持有期内，投资组合的
$$X=\sum_{j=1}^d w_j X_j$$
衡量风险现在包括确定分布函数 $F$ (或其泛函，例如均值、方差、 $\alpha$-分位数 $F^{\leftarrow}(\alpha)=$ $\inf x \in \mathbb{R}: F(x) \geq \alpha)$.
• 为此，我们需要一个适当校准的联合模型 $\boldsymbol{X}=\left(X_1, \ldots, X_d\right)$. 的统计估计 $F$ 或其功能之一是根据 对该模型的历史观察获得的。
什么是马币? Kloman (1990) 写道：
“RM 是一种与末来事件可能造成不利影响的可能性一起生活的学科。”
$\Rightarrow$ 它是关于确保对末来事件的弹性。
请注意，金融公司并非被动/防御风险，银行和保险公司主动/愿意承担风险，因为他们寻求回报。RM因此 属于他们的核心竞争力。
管理风险涉及什么?
出于监管目的（遵守监管机构）和经济资本目的（作为公司生存）确定持有以吸收损失的资本。
• 确保投资组合多元化。
• 根据风险回报考虑优化投资组合。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 金融代写|量化风险管理代写Quantitative Risk Management代考|BUSA90315

statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Market Risk

Market risk is risk associated with changing asset values. Market risk is most often associated with assets that trade in liquid financial markets, such as stocks and bonds. During trading hours, the prices of stocks and bonds constantly fluctuate. An asset’s price will change as new information becomes available and investors reassess the value of that asset. An asset’s value can also change due to changes in supply and demand.

All financial assets have market risk. Even if an asset is not traded on an exchange, its value can change over time. Firms that use mark-to-market accounting recognize this change explicitly. For these firms, the change in value of exchange-traded assets will be based on market prices. Other assets will either be marked to model -that is, their prices will be determined based on financial models with inputs that may include market prices-or their prices will be based on broker quotes – that is, their prices will be based on the price at which another party expresses their willingness to buy or sell the assets. Firms that use historical cost accounting, or book value accounting, will normally only realize a profit or a loss when an asset is sold. Even if the value of the asset is not being updated on a regular basis, the asset still has market risk. For this reason, most firms that employ historical cost accounting will reassess the value of their portfolios when they have reason to believe that there has been a significant change in the value of their assets.

For most financial instruments, we expect price changes to be relatively smooth and continuous most of the time, and large and discontinuous rarely. Because of this, market risk models often involve continuous distribution. Market risk models can also have a relatively high frequency (i.e., daily or even intraday). For many financial instruments, we will have a large amount of historical market data that we can use to evaluate market risk.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Credit Risk

Credit risk is the risk that one party in a financial transaction will fail to pay the other party. Credit risk can arise in a number of different settings. Firms may extend credit to suppliers and customers. Credit card debt and home mortgages create credit risk. One of the most common forms of credit risk is the risk that a corporation or government will fail to make interest payments or to fully repay the principal on bonds they have issued. This type of risk is known as default risk, and in the case of national governments it is also referred to as sovereign risk. Defaults occur infrequently, and the simplest models of default risk are based on discrete distributions. Although bond markets are large and credit rating agencies have been in existence for a long time, default events are rare. Because of this, we have much less historical data to work with when developing credit models, compared to market risk models.

For financial firms, counterparty credit risk is another important source of credit risk. While credit risk always involves two counterparties, when risk managers talk about counterparty credit risk they are usually talking about the risk arising from a significant long-term relationship between two counterparties. Prime brokers will often provide loans to investment firms, provide them with access to emergency credit lines, and allow them to purchase securities on margin. Assessing the credit risk of a financial firm can be difficult, time consuming, and costly. Because of this, when credit risk is involved, financial firms often enter into long-term relationships based on complex legal contracts. Counterparty risk specialists help design these contracts and play a lead role in assessing and monitoring the risk of counterparties.

Derivatives contracts can also lead to credit risk. A derivative is essentially a contract between two parties, that specifies that certain payments be made based on the value of an underlying security or securities. Derivatives include futures, forwards, swaps, and options. As the value of the underlying asset changes, so too will the value of the derivative. As the value of the derivative changes, so too will the amount of money that the counterparties owe each other. This leads to credit risk.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Enterprise Risk

The enterprise risk management group of a firm, as the name suggests, is responsible for the risk of the entire firm. At large financial firms, this often means overseeing market, credit, liquidity, and operations risk groups, and combining information from those groups into summary reports. In addition to this aggregation role, enterprise risk management tends to look at overall business risk. Large financial companies will often have a number of business units (e.g., capital markets, corporate finance, commercial banking, retail banking, asset management, etc.). Some of these business units will work very closely with risk management (e.g. capital markets, asset management), while others may have very little day-to-day interaction with risk (e.g. corporate finance). Regardless, enterprise risk management would assess how each business unit contributes to the overall profitability of the firm in order to assess the overall risk to the firm’s revenue, income, and capital.

Operational risk is risk arising from all aspects of a firm’s business activities. Put simply, it is the risk that people will make mistakes and that systems will fail. Operational risk is a risk that all financial firms must deal with.

Just as the number of activities that businesses carry out is extremely large, so too are the potential sources of operational risk. That said, there are broad categories on which risk managers tend to focus. These include legal risk (most often risk arising from contracts, which may be poorly specified or misinterpreted), systems risk (risk arising from computer systems) and model risk (risk arising from pricing and risk models, which may contain errors, or may be used inappropriately).

As with credit risk, operational risk tends to be concerned with rare but significant events. Operational risk presents additional challenges in that the sources of operational risk are often difficult to identify, define, and quantify.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 金融代写|量化风险管理代写Quantitative Risk Management代考|MKTG 7023

statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Intrinsic and Extrinsic Risk

Some financial professionals talk about risk versus uncertainty. A better approach might be to contrast intrinsic risk and extrinsic risk.

When evaluating financial instruments, there are some risks that we consider to be intrinsic. No matter how much we know about the financial instrument we are evaluating, there is nothing we can do to reduce this intrinsic risk (other than reducing the size of our investment).

In other circumstances risk is due only to our own ignorance. In theory, this extrinsic risk can be eliminated by gathering additional information through research and analysis.

As an example, an investor in a hedge fund may be subject to both extrinsic and intrinsic risk. A hedge fund investor will typically not know the exact holdings of a hedge fund in which they are invested. Not knowing what securities are in a fund is extrinsic risk.

For various reasons, the hedge fund manager may not want to reveal the fund’s holdings, but, at least in theory, this extrinsic risk could be eliminated by revealing the fund’s holdings to the investor. At the same time, even if the investor did know what securities were in the fund, the returns of the fund would still not be fully predictable because the returns of the securities in the fund’s portfolio are inherently uncertain. This inherent uncertainty of the security returns represents intrinsic risk and it cannot be eliminated, no matter how much information is provided to the investor.

Interestingly, a risk manager could reduce a hedge fund investor’s extrinsic risk by explaining the hedge fund’s risk guidelines. The risk guidelines could help the investor gain a better understanding of what might be in the fund’s portfolio, without revealing the portfolio’s precise composition.

Differentiating between these two fundamental types of risk is important in financial risk management. In practice, financial risk management is as much about reducing extrinsic risk as it is about managing intrinsic risk.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk and Standard Deviation

At the start of this chapter, we said that risk could be defined in terms of possible deviations from expectations. This definition is very close to the definition of standard deviation in statistics. The variance of a random variable is the expected value of squared deviations from the mean, and standard deviation is just the square root of variance. This is indeed very close to our definition of risk, and in finance risk is often equated with standard deviation.

While the two definitions are similar, they are not exactly the same. Standard deviation only describes what we expect the deviations will look like on average. Two random variables can have the same standard deviation, but very different return profiles. As we will see, risk managers need to consider other aspects of the distribution of expected deviations, not just its standard deviation.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|WHAT IS FINANCIAL RISK MANAGEMENT

In finance and in this book, we often talk about risk management, when it is understood that we are talking about financial risk management. Risk managers are found in a number of fields outside of finance, including engineering, manufacturing, and medicine.

When civil engineers are designing a levee to hold back flood waters, their risk analysis will likely include a forecast of the distribution of peak water levels. An engineer will often describe the probability that water levels will exceed the height of the levee in terms similar to those used by financial risk managers to describe the probability that losses in a portfolio will exceed a certain threshold. In manufacturing, engineers will use risk management to assess the frequency of manufacturing defects. Motorola popularized the term Six Sigma to describe its goal to establish a manufacturing process where manufacturing defects were kept below $3.4$ defects per million. (Confusingly the goal corresponds to $4.5$ standard deviations for a normal distribution, not 6 standard deviations, but that’s another story.) Similarly, financial risk managers will talk about big market moves as being three-sigma events or six-sigma events. Other areas of risk management can be valuable sources of techniques and terminology for financial risk management.

Within this broader field of risk management, though, how do we determine what is and is not financial risk management? One approach would be to define risk in terms of organizations, to say that financial risk management concerns itself with the risk of financial firms. By this definition, assessing the risks faced by Goldman Sachs or a hedge fund is financial risk management, whereas assessing the risks managed by the Army Corps of Engineers or NASA is not. A clear advantage to this approach is that it saves us from having to create a long list of activities that are the proper focus of financial risk management. The assignment is unambiguous. If a task is being performed by a financial firm, it is within the scope of financial risk management. This definition is future proof as well. If HSBC, one of the world’s largest financial institutions, starts a new business line tomorrow, we do not have to ask ourselves if this new business line falls under the purview of financial risk management. Because HSBC is a financial firm, any risk associated with the new business line would be considered financial risk.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 金融代写|量化风险管理代写Quantitative Risk Management代考|FINC6023

statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|量化风险管理代写Quantitative Risk Management代考|OVERVIEW OF FINANCIAL RISK MANAGEMENT

Imagine you are a chef at a restaurant. You’ve just finished preparing eggs benedict for a customer. The eggs are cooked perfectly, the hollandaise sauce has just the right mix of ingredients, and it all sits perfectly on the plate. The presentation is perfect! You’re so proud of the way this has turned out that you decide to deliver the dish to the customer yourself. You place the plate in front of the customer, and she replies, “This looks great, but I ordered a filet mignon, and you forgot my drink.”

Arguably, the greatest strength of modern financial risk management is that it is highly objective. It takes a scientific approach, using math and statistics to measure and evaluate financial products and portfolios. While these mathematical tools can be very powerful, they are simply that-tools. If we make unwarranted assumptions, apply models incorrectly, or present results poorly – or if our findings are ignored – then the most elegant mathematical models in the world will not help us. The eggs might be perfect, but that’s irrelevant if the customer ordered a steak.

This is not a new idea, Vitruvius, a famous Roman architect wrote, “Neque enim ingenium sine disciplina aut disciplina sine ingenio perfectum artificem potest efficere”, which roughly translates to “Neither genius without knowledge, nor knowledge without genius, will make a perfect artist.” Applying this to risk management, we might say, “Neither math without knowledge of financial markets, nor knowledge of financial markets without math, will make a perfect risk manager.”

Before we get to the math and statistics, then, we should take a step back and look at risk management more broadly. Before delving into the models, we explore the following questions: What is risk management? What is the proper role for a risk manager within a financial organization? What do risk managers actually do on a day-to-day basis?

We end this chapter with a brief history of risk management. As you will see, risk management has made many positive contributions to finance, but it is far from being a solved problem.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|WHAT IS RISK

Before we can begin to describe what financial risk managers do, we need to understand what financial risk $i$. In finance, risk arises from uncertainty surrounding future profits or returns. There are many ways to define risk, and we may change the definition slightly, depending on the task at hand.

In everyday speech, the word risk is associated with the possibility of negative outcomes. For something to be risky, the final outcome must be uncertain and there must be some possibility that the final outcome will have negative consequences. While this may seem obvious, some popular risk measures treat positive and negative outcomes equally, while others focus only negative outcomes. For this reason, in order to avoid any ambiguity when dealing specifically with negative outcomes, risk managers will often talk about downside risk.
Risk is often defined relative to expectations. If we have one investment with a $50 / 50$ chance of earning $\$ 0$or$\$200$, and a second investment with a $50 / 50$ chance of earning $\$ 400$or$\$600$, are both equally risky? The first investment earns $\$ 100$on average, and the second$\$500$, but both have a $50 / 50$ chance of being $\$ 100$above or below this expected value. Because the deviations from expectations are equal, many risk managers would consider the two investments to be equally risky. By this logic, the second investment is more attractive because it has a higher expected return, not because it is less risky. It is also important to note that risk is about possible deviations from expectations. If we expect an investment to make$\$1$ and it does make $\$ 1$, the investment was not necessarily risk free. If there were any possibility that the outcome could have been something other than$\$1$, then the investment was risky.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Absolute, Relative, and Conditional Risk

There may be no better way to understand the limits of financial risk management-why and where it may fail or succeed – than to understand the difference between absolute, relative, and conditional risk.

Financial risk managers are often asked to assign probabilities to various financial outcomes. What is the probability that a bond will default? What is the probability that an equity index will decline by more than $10 \%$ over the course of a year? These types of predictions, where risk managers are asked to assess the total or absolute risk of an investment, are incredibly difficult to make. As we will see, assessing the accuracy of these types of predictions, even over the course of many years, can be extremely difficult.

It is often much easier to determine relative risk than to measure risk in isolation. Bond ratings are a good example. Bond ratings can be used to assess absolute risk, but they are on much surer footing when used to assess relative risk. The number of defaults in a bond portfolio might be much higher or lower next year depending on the state of the economy and financial markets. No matter what happens, though, a portfolio consisting of a large number of AAA-rated bonds will almost certainly have fewer defaults than a portfolio consisting of a large number of C-rated bonds. Similarly, it is much easier to say that emerging market equities are riskier than U.S. equities, or that one hedge fund is riskier than another hedge fund.
What is the probability that the S\&P 500 will be down more than $10 \%$ next year? What is the probability that a particular U.S. large-cap equity mutual fund will be down more than $8 \%$ next year? Both are very difficult questions. What is the probability that this same mutual fund will be down more than $8 \%$, if the S\&P 500 is down more than $10 \%$ ? This last question is actually much easier to answer. What’s more, these types of conditional risk forecasts immediately suggest ways to hedge and otherwise mitigate risk.

Given the difficulty of measuring absolute risk, risk managers are likely to be more successful if they limit themselves to relative and conditional forecasts, when possible. Likewise, when there is any ambiguity about how a risk measure can be interpreted —as with bond ratings – encouraging a relative or conditional interpretation is likely to be in a risk manager’s best interest.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 金融代写|量化风险管理代写Quantitative Risk Management代考|FINC6023

statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Examples of Parametric Distributions

Elliptical distributions: this class of distributions includes the Gaussian distribution and the $t$-distribution.

• The random variable $X$ is said to have a Gaussian distribution if its density (with mean $\mu$ and variance $\sigma^{2}$ ) is such that
$$f_{X}(x)=\frac{1}{(2 \pi)^{1 / 2} \sigma} \exp \left(-\frac{1}{2 \sigma^{2}}(x-\mu)^{-2}\right) .$$
This distribution is symmetrical and decreases very quickly towards zero. When $\mu=0$ and $\sigma=1$, then its kurtosis is equal to 3 . This value is used as a benchmark to decide if any distribution has low tail behaviour (kurtosis less than 3 ) or high tail behaviour (kurtosis bigger than 3 ).
• The $t$-distribution density is proportional to:
$$f_{X}(x)=\frac{1}{1+\left(x^{2} / \nu\right)^{(v+1) / 2}} .$$
The $t$-distribution’s tail becomes heavier as $v$ increases ( $v$ is the number of degrees of freedom). This distribution is not easy to use in finance because the $v$ parameter is an integer, rather than a continuous parameter and limits the flexibility of its using.
• Other distributions can be used whose properties are complementary to the two previous distributions because they have more parameters. In finance, we are interested in heavy tailed distribution functions with high kurtosis because it is more prone to extreme values. For instance, the GED distribution can be considered. The density of a GED random variable normalised to have a mean of zero and a variance of one is given by:
$$f(z)=\frac{\operatorname{vexp}\left[-1 /\left.2||_{\lambda}\right|^{v}\right]}{\lambda 2^{1+1 / v} \Gamma(1 / v)},-\infty2, the distribution of z has thinner tails than the normal. This density appears more preferable to the Student- t distribution because v \in R^{+}. ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Non-parametric Modelling for a Distribution The non-parametric setting avoids the uncertainty on the choice of parametric densities and permits limiting the errors due to estimation procedure applied to estimate the parameters of the densities (Silverman 2018). Suppose we are given independent identically distributed real-valued observations \left(X_{1}, \cdots, X_{n}\right) with density f. We estimate f at a grid of points x_{1}, \cdots, x_{M}, for any arbitrary M fixed, and in particular here, we focus on estimation at a single point x. If f is smooth in a small neighbourhood [x-h, x+h] of x, the following approximation can be obtained:$$
2 h \cdot f(x) \approx \int_{x-h}^{x+h} f(u) d u=P(X \in[x-h, x+h])
$$by the mean value theorem. The right-hand side of (4.1.14) can be approximated by counting the number of X_{i} ‘s in the small interval of length 2 h, and then dividing by n. This is an histogram estimator with bincentre x and bandwidth 2 h. Let K(u)= \frac{1}{2} I(|u| \leq 1), where I(.) is the indicator function taking the value 1 when the event is true and zero otherwise. Then, the histogram estimator can be written:$$
\hat{f}{h}(x)=n^{-1} \sum{i=1}^{n} K_{h}\left(x-X_{i}\right)
$$where K_{h}(.)=h^{-1} K_{h}(. / h). The expression (4.1.15) is called the kernel density estimator of f(x) with kernel K(u)=\frac{1}{2} I(|u| \leq 1) and bandwidth h. The step function kernel weights each observation inside the window equally, even though observations closer to x should possess better information than more distant ones. In addition the step function estimator is discontinuous in x, which is unattractive given the smoothness assumption on f. Both objectives can be satisfied by choosing a smoother “window function” K as kernel, i.e., one for which K(u) \rightarrow 0 as |u| \rightarrow 1. A kernel is a piecewise continuous function, symmetric around zero, integrating to one:$$
K(u)=K(-u) ; \int K(u) d u=1 .
f(z)=\frac{\operatorname{vexp}\left[-1 /\left.2|| _{\lambda}\right|^{v}\right]}{\lambda 2^{1+1 / v} \Gamma(1 / v)},-\infty2,吨H和d一世s吨r一世b在吨一世○n○F和H一个s吨H一世nn和r吨一个一世ls吨H一个n吨H和n○r米一个l.吨H一世sd和ns一世吨是一个pp和一个rs米○r和pr和F和r一个bl和吨○吨H和小号吨在d和n吨−吨d一世s吨r一世b在吨一世○nb和C一个在s和v \in R^{+}$。 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Non-parametric Modelling for a Distribution 非参数设置避免了参数密度选择的不确定性，并允许限制由于用于估计密度参数的估计程序而导致的误差（Silverman 2018）。 假设给定独立的同分布实值观测(X1,⋯,Xn)有密度F. 我们估计F在点的网格上X1,⋯,X米, 对于任何任意米固定的，特别是在这里，我们专注于单点估计X. 如果F在一个小街区很顺利[X−H,X+H]的X，可以得到以下近似： 2H⋅F(X)≈∫X−HX+HF(在)d在=磷(X∈[X−H,X+H]) 由中值定理。(4.1.14) 的右边可以通过计算X一世的在长度的小区间内2H，然后除以n. 这是一个带有 bincentre 的直方图估计器X和带宽2H. 让ķ(在)= 12我(|在|≤1)， 在哪里我(.)是指示函数，当事件为真时取值为 1，否则取值为 0。然后，直方图估计量可以写成： F^H(X)=n−1∑一世=1nķH(X−X一世) 在哪里ķH(.)=H−1ķH(./H). 表达式 (4.1.15) 称为核密度估计F(X)带内核ķ(在)=12我(|在|≤1)和带宽H. 阶跃函数内核对窗口内的每个观察值进行平均加权，即使观察值更接近X应该拥有比更远的信息更好的信息。此外，阶跃函数估计器在X，考虑到平滑度假设，这是没有吸引力的F. 这两个目标都可以通过选择更平滑的“窗口函数”来满足ķ作为内核，即一个ķ(在)→0 为|在|→1. 核是一个分段连续函数，围绕零对称，积分为一： ķ(在)=ķ(−在);∫ķ(在)d在=1. ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Shift of a Distribution 为了改变分布FX随机变量X失真函数G应用于累积分布函数FX. 这样的功能G定义在[0,1]→[0;1]这样G(0)=0和G(1)=1，并且是一个连续递增的函数（Wang and Young 1998；Wang 2000）。 失真函数源于经验观察，即人们不会将风险评估为不同结果的实际概率的线性函数，而是作为非线性失真函数。它用于通过重新加权原始分布将损失分布的概率转换为另一个概率分布。这种转变增加了对理想事件的权重，并降低了其他事件的权重。不同的扭曲G已在文献中提出。表中提供了一些功能4.1, 其中参数ķ和C代表置信水平和风险厌恶程度。 什么时候G是凹函数，它的一阶导数G′是一个增函数，G′(小号X(X))在哪里小号X=磷[X>X]是一个递减函数1在X和G′(小号X(X))表示一个加权系数，它在加载不良事件概率的同时，对期望事件的概率进行折现。失真算子的第一种方法是G一个(在)=披[披−1(在)+一个]， 在哪里披是高斯累积分布。在风险度量方面，最后一个函数应用相同的偏好视角来量化与收益和风险相关的风险。因此，风险经理使用相同的功能评估与上行和下行风险相关的风险G意味着对这两种效应进行对称考虑，因为 失真。此外，它对损失和收益产生相同的置信水平，这意味着与损失和收益相关的风险厌恶程度相同。 在图。4.3介绍了之前引入的失真函数对逻辑分布的影响。我们注意到在这种失真函数下，失真分布总是对称的，并且我们观察到初始分布的模式向左移动。 为了避免对称性问题，可以使用以下失真函数：G一世(在)=在+ķ一世(在−在2)为了ķ∈]0,1]和∀一世∈1,2. 从风险度量的角度来看，一个模型的损失和收益相对于参数的值是不同的ķ一世,一世=1,2 。因此，上行和下行风险以不同的方式建模。尽管如此，参数的校准ķ一世,一世=1,2不简单。 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 ## 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 ## 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 ## 广义线性模型代考 广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 ## 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。 ## 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 ## 时间序列分析代写 随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。 ## 回归分析代写 多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。 ## MATLAB代写 MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|BUSA90315 如果你也在 怎样代写量化风险管理Quantitative Risk Management这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。 项目管理中的定量风险管理是将风险对项目的影响转换为数字的过程。这种数字信息经常被用来确定项目的成本和时间应急措施。 statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。 我们提供的量化风险管理Quantitative Risk Management及其相关学科的代写，服务范围广, 其中包括但不限于: • Statistical Inference 统计推断 • Statistical Computing 统计计算 • Advanced Probability Theory 高等概率论 • Advanced Mathematical Statistics 高等数理统计学 • (Generalized) Linear Models 广义线性模型 • Statistical Machine Learning 统计机器学习 • Longitudinal Data Analysis 纵向数据分析 • Foundations of Data Science 数据科学基础 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk Management in Essence A hyperbola forms the efficient frontier if no risk-free asset is available (assumption that most portfolio manager considers as being closer to reality). Assuming the existence of a risk-free asset, the efficient frontier is a straight line. Formally, for a risk level given$q \in[0, \infty)$, the efficient frontier is obtained by minimising the following expression: $$w^{T} \Sigma w-q * R^{T} w$$ where •$w$is a vector of portfolio weights and$\sum_{i} w_{i}=1$. Note that negative weights indicate the sale of a security.; •$\Sigma$is the covariance matrix for the returns on the assets in the portfolio; •$q \geq 0$is the risk level factor, •$R$is a vector of expected returns, •$w^{T} \Sigma w$is the variance of portfolio’s return, •$R^{T} w$is the expected return of the portfolio. Remark 3.2.2 The two mutual fund theorem (Merton 1972) states that any portfolio on the efficient frontier can be generated by holding a combination of any two given portfolios on the frontier; the latter two given portfolios are the “mutual funds” in the theorem’s name. So in the absence of a risk-free asset, an investor can achieve any desired efficient portfolio even if all that is accessible is a pair of efficient mutual funds. If the location of the desired portfolio on the frontier is between the locations of the two mutual funds, both mutual funds will be held in positive quantities. If the desired portfolio is outside the range spanned by the two mutual funds, then one of the mutual funds must be sold short (held in negative quantity) while the size of the investment in the other mutual fund must be greater than the amount available for investment (the excess being funded by the borrowing from the other fund). ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk-Free Asset and the Capital Allocation Line The risk-free asset is the asset that pays a risk-free rate assuming that this asset exists. In practice, short-term government securities are used as a risk-free asset, because they pay a fixed rate of interest and have exceptionally low default risk. The risk-free asset is constant and is mechanically uncorrelated with any other asset. Consequently, when combined with any other asset or portfolio of assets, the change in return is linearly related to the change in risk as the proportions in the combination vary. When a risk-free asset is introduced, the half-line shown in the figure is the new efficient frontier. It is tangent to the hyperbola at the pure risky portfolio with the highest Sharpe ratio. Its vertical intercept represents a portfolio with$100 \%$of holdings in the risk-free asset; the tangency with the hyperbola represents a portfolio with no risk-free holdings and$100 \%$of assets held in the portfolio occurring at the tangency point; points between those points are portfolios containing positive amounts of both the risky tangency portfolio and the risk-free asset; and points on the half-line beyond the tangency point are leveraged portfolios involving negative holdings of the risk-free asset (the latter has been sold short-in other words, the investor has borrowed at the risk-free rate) and an amount invested in the tangency portfolio equal to more than$100 \%$of the investor’s initial capital. This efficient half-line is called the capital allocation line (CAL), and its formula can be shown to be $$E\left(R_{C}\right)=R_{F}+\sigma_{C} \frac{E\left(R_{P}\right)-R_{F}}{\sigma_{P}}$$ In this formula$\mathrm{P}$is the sub-portfolio of risky assets at the tangency with the Markowitz curve,$F$is the risk-free asset, and$C$is a combination of portfolios$P$and$F$. By the diagram, the introduction of the risk-free asset as a possible component of the portfolio has improved the range of risk-expected return combinations available, because everywhere except at the tangency portfolio the half-line gives a higher expected return than the hyperbola does at every possible risk level. The fact that all points on the linear efficient locus can be achieved by a combination of holdings of the risk-free asset and the tangency portfolio is known as the one mutual fund theorem, where the mutual fund referred to is the tangency portfolio. ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk Management Through MPT The specific risk is the risk associated with individual assets. As introduced above, these risks can be reduced through diversification. The specific risk is diversifiable, unique, unsystematic, and therefore traditionally denoted idiosyncratic risk. The systematic risk refers to the risk common to all securities. The systematic risk cannot be diversified, assuming a single market. The systematic risk is therefore equivalent to the risk of the market portfolio. Since a security will be purchased only if it improves the risk-expected return characteristics of the market portfolio, the relevant measure of the risk of a security is the risk it adds to the market portfolio, and not its risk in isolation. In this context, the volatility of the asset and its correlation with the market portfolio are historically observed and are therefore given. (There are several approaches to asset pricing that attempt to price assets by modelling the stochastic properties of the moments of assets’ returns – these are broadly referred to as conditional asset pricing models.) Systematic risks within one market can be managed through a strategy of using both long and short positions within one portfolio, creating a “market neutral” portfolio. Market neutral portfolios, therefore will have a correlations of zero. ## 量化风险管理代考 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk Management in Essence 如果没有无风险资产可用，则双曲线形成有效边界（大多数投资组合经理认为更接近现实的假设）。假设存在无风险资产，则有效边界是一条直线。正式地，对于给定的风险水平q∈[0,∞)，通过最小化以下表达式获得有效边界： 在吨Σ在−q∗R吨在 在哪里 • 在是投资组合权重的向量，并且∑一世在一世=1. 请注意，负权重表示出售证券。 • Σ是投资组合中资产收益的协方差矩阵； • q≥0是风险水平因子， • R是预期收益的向量， • 在吨Σ在是投资组合收益的方差， • R吨在是投资组合的预期收益。 备注 3.2.2 两个共同基金定理 (Merton 1972) 指出，有效前沿上的任何投资组合都可以通过在前沿上持有任意两个给定投资组合来产生；后两个给定的投资组合是定理名称中的“共同基金”。因此，在没有无风险资产的情况下，即使只有一对高效的共同基金，投资者也可以实现任何期望的高效投资组合。如果边界上所需投资组合的位置在两个共同基金的位置之间，则两个共同基金都将以正数持有。如果所需的投资组合超出两个共同基金的范围， ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk-Free Asset and the Capital Allocation Line 无风险资产是假设该资产存在时支付无风险利率的资产。在实践中，短期政府证券被用作无风险资产，因为它们支付固定利率并且违约风险极低。无风险资产是恒定的，并且与任何其他资产在机械上不相关。因此，当与任何其他资产或资产组合组合时，随着组合中的比例变化，收益变化与风险变化呈线性相关。 当引入无风险资产时，图中所示的半线即为新的有效边界。它与夏普比率最高的纯风险投资组合的双曲线相切。它的垂直截距代表一个投资组合100%无风险资产的持有量；与双曲线的相切表示没有无风险持有的投资组合，并且100%在切点发生的投资组合中持有的资产；这些点之间的点是包含正量风险切线投资组合和无风险资产的投资组合；切点以外的半线上的点是杠杆投资组合，涉及负持有无风险资产（后者已被卖空，换句话说，投资者以无风险利率借入）和投资金额在相切投资组合中大于等于100%投资者的初始资本。这条有效的半线称为资本配置线（CAL），其公式可表示为 和(RC)=RF+σC和(R磷)−RFσ磷 在这个公式中磷是与马科维茨曲线相切的风险资产的子投资组合，F是无风险资产，并且C是投资组合的组合磷和F. 从图中可以看出，将无风险资产作为投资组合的一个可能组成部分，提高了可用的风险预期回报组合的范围，因为除了切线投资组合之外，在任何地方，半线都比双曲线提供了更高的预期回报在每个可能的风险水平上都这样做。线性有效轨迹上的所有点都可以通过持有无风险资产和切线投资组合来实现，这一事实被称为单一共同基金定理，其中所指的共同基金是切线投资组合。 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk Management Through MPT 特定风险是与单个资产相关的风险。如上所述，这些风险可以通过多元化来降低。特定风险是可分散的、独特的、非系统性的，因此传统上称为异质风险。这 系统性风险是指所有证券共有的风险。假设单一市场，系统性风险无法分散。因此，系统性风险等同于市场组合的风险。 由于证券只有在改善市场投资组合的风险预期收益特征时才会被购买，证券风险的相关衡量标准是它增加市场投资组合的风险，而不是孤立的风险。在这种情况下，资产的波动性及其与市场投资组合的相关性是历史上观察到的，因此是给定的。（有几种资产定价方法试图通过对资产回报时刻的随机属性进行建模来为资产定价——这些被广泛称为条件资产定价模型。） 可以通过在一个投资组合中同时使用多头和空头头寸的策略来管理一个市场内的系统性风险，从而创建一个“市场中性”的投资组合。因此，市场中性投资组合的相关性为零。 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 ## 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 ## 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 ## 广义线性模型代考 广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 ## 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。 ## 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 ## 时间序列分析代写 随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。 ## 回归分析代写 多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。 ## MATLAB代写 MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|MINE7034 如果你也在 怎样代写量化风险管理Quantitative Risk Management这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。 项目管理中的定量风险管理是将风险对项目的影响转换为数字的过程。这种数字信息经常被用来确定项目的成本和时间应急措施。 statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。 我们提供的量化风险管理Quantitative Risk Management及其相关学科的代写，服务范围广, 其中包括但不限于: • Statistical Inference 统计推断 • Statistical Computing 统计计算 • Advanced Probability Theory 高等概率论 • Advanced Mathematical Statistics 高等数理统计学 • (Generalized) Linear Models 广义线性模型 • Statistical Machine Learning 统计机器学习 • Longitudinal Data Analysis 纵向数据分析 • Foundations of Data Science 数据科学基础 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Semi-Interquartile Deviation The semi-interquartile deviation or range${ }^{2}$corresponds to one-half of the interquartile range, i.e., the difference between the third quartile$(\mathrm{Q} 3)$and the first$(\mathrm{Q} 1)$and the coefficient of quartile variation is the interquartile range divided by the second quartile. Formally, the semi-interquartile range, measuring the dispersion, is expressed as follows: $$S I=\frac{(Q 3-Q 1)}{2}$$ while the coefficient of quartile variation is expressed as follows: $$S I=\frac{(Q 3-Q 1)}{Q 2}$$ In a symmetric distribution, contrary to a skewed distribution, an interval stretching from one semi-interquartile range below the median to one semi-interquartile above the median will contain half of the values. It is interesting to mention that semi-interquartile range is barely affected by extreme values, as a consequence it is a good dispersion measure for skewed distributions. However, it is more subject to sampling fluctuation in the Gaussian case than is the standard deviation and therefore not often used for data that are approximately normally distributed. However, this class of risk measure exhibits the major drawbacks of assuming distribution with specific characteristics such as symmetry and of not take into account losses occurring with small probabilities. ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Mean Absolute Difference Assuming the probability space defined in introduction, let$X$and$Y$be two iid random variables following the same distribution. The mean absolute difference (MAD) is given by the average of the differences of all possible pairs of variatevalues, taken regardless of their sign. It is formally defined as follows: $$\mathrm{MAD}:=E[|X-Y|] .$$ Let$x_{1}, \ldots, x_{n}$and$y_{1}, \ldots, y_{n}$be two sets of respective realisations of random variables$X$and$Y$. For a random sample of size$n$of a population uniformly distributed, by the law of total expectation${ }^{3}$the mean absolute difference of the sample$y_{i}, i=1$to$n$corresponds to the arithmetic mean of the absolute value of all possible differences, $$\mathrm{MAD}=E[|X-Y|]=E_{X}\left[E_{X|Y|}[|X-Y|]\right]=\frac{1}{n^{2}} \sum_{i=1}^{n} \sum_{j=1}^{n}\left|y_{i}-y_{j}\right| .$$ If$Y$follows a discrete probability function$f(y)$, where$y_{i}, i=1$to$n$are the values with non-zero probabilities: $$\mathrm{MAD}=\sum_{i=1}^{n} \sum_{j=1}^{n} f\left(y_{i}\right) f\left(y_{j}\right)\left|y_{i}-y_{j}\right|$$ In the continuous case, let$f(x)$be the probability density function, then, $$\mathrm{MAD}=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} f(x) f(y)|x-y| d x d y$$ Let$F(x)$, absolutely continuous, be the cumulative distribution function associated with$f(x)$with quantile function$F^{-1}(x)$, then, since$f(x)=d F(x) / d x$and$F^{-1}(x)=x$, it follows that: $$\mathrm{MAD}=\int_{0}^{1} \int_{0}^{1}\left|F_{1}^{-1}-F_{2}^{-1}\right| d F_{1} d F_{2} .$$ ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Modern Portfolio Theory Modern portfolio theory (Markowitz 1952) is a mathematical framework for constituting a portfolio of assets such that the expected return is maximised for a given level of risk, here the variance. The difference with what we discussed before is that both risk and return of an asset should not be assessed on their own, but by how it contributes to a portfolio’s overall risk and return. Modern portfolio theory assumes that investors are risk averse that for the same expected return given by two portfolios, investors will prefer the less risky one. As a consequence, an investor may only accept on increased exposure if this one is compensated by higher expected returns. Conversely, an investor who is willing higher expected returns must face larger exposures. The exact trade-off will be the same for all investors, but different investors will evaluate the trade-off differently based on individual risk aversion characteristics. This implies that a rational investor would not invest in a portfolio if it exists a second portfolio with a more favourable risk-expected return profile-i.e., if for that level of risk an alternative portfolio exists that has better expected returns. Under the model: • Portfolio return is the proportion-weighted combination of the constituent assets’ returns. • Portfolio volatility is a function of the correlations$\rho_{i j}$of the component assets, for all asset pairs$(i, j)$. The expected return is given by the following equation: $$\mathrm{E}\left(R_{p}\right)=\sum_{i} w_{i} \mathrm{E}\left(R_{i}\right)$$ where$R_{p}$is the return on the portfolio,$R_{i}$is the return on asset$i$, and$w_{i}$is the weighting of component asset$i$(that is, the proportion of asset ”$i$” in the portfolio). The portfolio return variance is provided by the following equation: $$\sigma_{p}^{2}=\sum_{i} w_{i}^{2} \sigma_{i}^{2}+\sum_{i} \sum_{j \neq i} w_{i} w_{j} \sigma_{i} \sigma_{j} \rho_{i j}$$ where$\sigma_{i}$is the standard deviation of the returns on asset$i$, and$\rho_{i j}$is the correlation coefficient between the returns on assets$i$and$j$. It is also possible to rewrite the expression as: $$\sigma_{p}^{2}=\sum_{i} \sum_{j} w_{i} w_{j} \sigma_{i} \sigma_{j} \rho_{i j}$$ where$\rho_{i j}=1$for$i=j$, or $$\sigma_{p}^{2}=\sum_{i} \sum_{j} w_{i} w_{j} \sigma_{i j}$$ where$\sigma_{i j}=\frac{\sigma_{i} \sigma_{i}}{\rho_{i}}$is the covariance of the returns of the two assets. ## 量化风险管理代考 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Semi-Interquartile Deviation 半四分位差或范围2对应四分位间距的二分之一，即第三个四分位差(问3)和第一个(问1)四分位变异系数是四分位间距除以第二个四分位。形式上，测量离散度的半四分位距表示如下： 小号我=(问3−问1)2 而四分位变异系数表示如下： 小号我=(问3−问1)问2 在对称分布中，与偏态分布相反，从低于中位数一个半四分位数范围延伸到高于中位数一个半四分位数的区间将包含一半的值。 有趣的是，半四分位距几乎不受极值的影响，因此它是偏态分布的良好分散度量。但是，在高斯情况下，它比标准偏差更容易受到采样波动的影响，因此不常用于近似正态分布的数据。 然而，这类风险度量的主要缺点是假设分布具有特定特征，例如对称性，并且没有考虑小概率发生的损失。 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Mean Absolute Difference 假设引言中定义的概率空间，让X和是是遵循相同分布的两个独立同分布随机变量。平均绝对差 (MAD) 由所有可能的变量值对的差异的平均值给出，无论它们的符号如何。它的正式定义如下： 米一个D:=和[|X−是|]. 让X1,…,Xn和是1,…,是n是随机变量的两组各自的实现X和是. 对于大小的随机样本n根据总期望定律，人口均匀分布3样本的平均绝对差是一世,一世=1至n对应于所有可能差异的绝对值的算术平均值， 米一个D=和[|X−是|]=和X[和X|是|[|X−是|]]=1n2∑一世=1n∑j=1n|是一世−是j|. 如果是遵循离散概率函数F(是)， 在哪里是一世,一世=1至n是具有非零概率的值： 米一个D=∑一世=1n∑j=1nF(是一世)F(是j)|是一世−是j| 在连续情况下，让F(X)为概率密度函数，则， 米一个D=∫−∞∞∫−∞∞F(X)F(是)|X−是|dXd是 让F(X)，绝对连续，是与相关的累积分布函数F(X)带分位数功能F−1(X)，那么，因为F(X)=dF(X)/dX和F−1(X)=X， 它遵循： 米一个D=∫01∫01|F1−1−F2−1|dF1dF2. ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Modern Portfolio Theory 现代投资组合理论（Markowitz 1952）是一个数学框架，用于构成资产组合，使得预期收益在给定的风险水平下最大化，这里是方差。与我们之前讨论的不同之处在于，资产的风险和回报不应单独评估，而应通过它对投资组合的整体风险和回报的贡献来评估。 现代投资组合理论假设投资者是风险厌恶的，即对于两个投资组合给出的相同预期回报，投资者会更喜欢风险较小的一个。因此，投资者可能只接受增加的风险敞口，前提是这一风险能够得到更高的预期回报。相反，愿意获得更高预期回报的投资者必须面临更大的风险敞口。所有投资者的确切权衡将是相同的，但不同的投资者会根据个人风险厌恶特征对权衡进行不同的评估。这意味着如果一个投资组合存在具有更有利的风险预期收益概况的第二个投资组合，即如果对于该风险水平存在具有更好预期收益的替代投资组合，则理性投资者不会投资该投资组合。 模型下： • 投资组合回报是成分资产回报的比例加权组合。 • 投资组合波动率是相关性的函数ρ一世j组件资产的数量，适用于所有资产对(一世,j). 预期回报由以下等式给出： 和(Rp)=∑一世在一世和(R一世) 在哪里Rp是投资组合的回报，R一世是资产回报率一世， 和在一世是组成资产的权重一世（即资产比例”一世”在投资组合中）。投资组合收益方差由以下等式提供： σp2=∑一世在一世2σ一世2+∑一世∑j≠一世在一世在jσ一世σjρ一世j 在哪里σ一世是资产回报率的标准差一世， 和ρ一世j是资产收益率之间的相关系数一世和j. 也可以将表达式重写为： σp2=∑一世∑j在一世在jσ一世σjρ一世j 在哪里ρ一世j=1为了一世=j， 或者 σp2=∑一世∑j在一世在jσ一世j 在哪里σ一世j=σ一世σ一世ρ一世是两种资产收益的协方差。 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 ## 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 ## 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 ## 广义线性模型代考 广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 ## 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。 ## 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 ## 时间序列分析代写 随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。 ## 回归分析代写 多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。 ## MATLAB代写 MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|PROJMGNT 5004 如果你也在 怎样代写量化风险管理Quantitative Risk Management这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。 项目管理中的定量风险管理是将风险对项目的影响转换为数字的过程。这种数字信息经常被用来确定项目的成本和时间应急措施。 statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management相关的作业也就用不着说。 我们提供的量化风险管理Quantitative Risk Management及其相关学科的代写，服务范围广, 其中包括但不限于: • Statistical Inference 统计推断 • Statistical Computing 统计计算 • Advanced Probability Theory 高等概率论 • Advanced Mathematical Statistics 高等数理统计学 • (Generalized) Linear Models 广义线性模型 • Statistical Machine Learning 统计机器学习 • Longitudinal Data Analysis 纵向数据分析 • Foundations of Data Science 数据科学基础 ## 金融代写|量化风险管理代写Quantitative Risk Management代考|Distance Between Representative Values Three main measures are constituting this group: • In statistics, the range is simply the difference between the highest and lowest value taken by the variable under consideration, but it might have a more complex meaning (see below). 1. For$n$independent and identically distributed continuous random variables$X_{1}, X_{2}, \ldots, X_{n}$with cumulative distribution function$F(x)$and probability density function$f(x)$, let$t$denote the range of a sample of size$n$from a population with distribution function$F(x)$. The range has cumulative distribution function (Gumbel 1947) $$G(t)=n \int_{-\infty}^{\infty} f(x)[F(x+t)-F(x)]^{n-1} \mathrm{~d} x$$ The mean range is given as follows (Hartley and David 1954): $$n \int_{0}^{1} F^{-1}\left[F^{n-1}-(1-F)^{n-1}\right] \mathrm{d} F$$ 2. For$n$non-identically distributed independent continuous random variables$X_{1}, X_{2}, \ldots, X_{n}$with cumulative distribution functions$F_{1}(x), F_{2}(x), \ldots$,$F_{n}(x)$and probability density functions$f_{1}(x), f_{2}(x), \ldots, f_{n}(x)$, the range has cumulative distribution function (Tsimashenka et al. 2012) $$G(t)=\sum_{i=1}^{n} \int_{-\infty}^{\infty} f_{i}(x) \prod_{j=1, j \neq i}^{n}\left[F_{j}(x+t)-F_{j}(x)\right] \mathrm{d} x .$$ 3. For$n$independent and identically distributed discrete random variables$X_{1}, X_{2}, \ldots, X_{n}$with cumulative distribution function$F(x)$and probability mass function$f(x)$the range of the$X_{i}$is the range of a sample of size$n$from a population with distribution function$F(x)$. The range has probability mass function as follows (Evans et al. 2006; Burr 1955; Abdel-Aty 1954; Siotani 1956): $$g(t)=\left{\begin{array}{l} \sum_{x=1}^{N}[f(x)]^{n} \ \sum_{x=1}^{N-1}\left(\begin{array}{l} {[F(x+t)-F(x-1)]^{n}} \ -[F(x+t)-F(x)]^{n} \ -[F(x+t-1)-F(x-1)]^{n} \ +[F(x+t-1)-F(x)]^{n} \end{array}\right) \quad t=0 \end{array} \quad t=1,2,3 \ldots, N-1 .\right.$$ ## 金融代写|量化风险管理代写Quantitative Risk Management代考|The Variance The variance and its square root, i.e., the standard deviation, constitute the most widely employed measures. The variance is defined as the expected value of the squared deviations of the data values from the mean, and thus simply measures the dispersion of the estimates around their mean value. Let$X$be a random variable defined on the probability space previously introduced, then the expected value of$X$, denoted by$E[X]$, is defined as the Lebesgue integral $$E[X]=\int_{\Omega} X(\omega) d \mathrm{P}(\omega) .$$ In our case, the expected value corresponds to the mean. Formally, the variance of a random variable$X$is the expected value of the squared deviation from the mean of$\mu=\mathrm{E}[X]$$$\operatorname{Var}(X)=\mathrm{E}\left[(X-\mu)^{2}\right]$$ The variance is also the second moment or second cumulant of a probability distribution that generates$X$. The variance is typically designated as$\operatorname{Var}(X), \sigma_{X}^{2}$,$\sigma^{2}. The expression for the variance can be expanded as follows: \begin{aligned} \operatorname{Var}(X) &=\mathrm{E}\left[(X-\mathrm{E}[X])^{2}\right] \ &=\mathrm{E}\left[X^{2}-2 X \mathrm{E}[X]+\mathrm{E}[X]^{2}\right] \ &=\mathrm{E}\left[X^{2}\right]-2 \mathrm{E}[X] \mathrm{E}[X]+\mathrm{E}[X]^{2} \ &=\mathrm{E}\left[X^{2}\right]-\mathrm{E}[X]^{2} \end{aligned} If the random variableX$follows a continuous distribution with probability density function$f(x)$, then the variance of$Xis given by \begin{aligned} \operatorname{Var}(X) &=\sigma^{2} \ &=\int(x-\mu)^{2} f(x) d x \ &=\int x^{2} f(x) d x-2 \mu \int x f(x) d x+\int \mu^{2} f(x) d x \ &=\int x^{2} f(x) d x-\mu^{2} \end{aligned} where\mu$is the expected value of$X$given by the following: $$\mu=\int x f(x) d x,$$ and where$x$is ranging over the range of$X$. ## 金融代写|量化风险管理代写Quantitative Risk Management代考|The Expected Absolute Deviation The expected absolute deviation (sometimes called the mean absolute deviation) is the sum of the absolute values of the deviations from the mean (of course this measure could be adapted to any other threshold, like 0 , the median or the mode, for example${ }^{1}$). The term average absolute deviation does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well. Thus, to uniquely identify the absolute deviation it is necessary to specify both the measure of deviation and the measure of central tendency. Unfortunately, the statistical literature has not yet adopted a standard notation, as both the mean absolute deviation around the mean and the median absolute deviation around the median have been denoted by their initials “MAD” in the literature, which may lead to confusion, since in general, they may have values considerably different from each other. The mean absolute deviation of a set$x_{1}, x_{2}, \ldots, x_{n}$issued of a r.v. X, is given by the following equation: $$\mathbb{E}(|X-m(X)|)=\frac{1}{n} \sum_{i=1}^{n}\left|x_{i}-m(X)\right|$$ where$m(X)$represent the chosen central tendency, usually the median, the mode, or the mean of the r.v. X. It is noteworthy to mention that the choice of the central tendency impacts the metric. The mean absolute deviation from the median is less than or equal to the mean absolute deviation from the mean. In fact, the mean absolute deviation from the median is always less than or equal to the mean absolute deviation from any other fixed number. The mean absolute deviation from the mean (denoted$\mu$in what follows) is less than or equal to the standard deviation; one way of proving this relies on Jensen’s inequality:$\phi(\mathbb{E}[Y]) \leq \mathbb{E}[\phi(Y)]$, where$\phi$is a convex function, this implies for$Y=|X-\mu| \mu\$ being the sample mean that:
$$\begin{gathered} \mathbb{E}(|X-\mu|)^{2} \leq \mathbb{E}\left(|X-\mu|^{2}\right) \ \mathbb{E}(|X-\mu|)^{2} \leq \operatorname{Var}(X) \end{gathered}$$

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Distance Between Representative Values

• 在统计学中，范围只是所考虑变量的最高值和最低值之间的差，但它可能具有更复杂的含义（见下文）。
1. 为了n独立同分布的连续随机变量X1,X2,…,Xn具有累积分布函数F(X)和概率密度函数F(X)， 让吨表示大小样本的范围n来自具有分布函数的总体F(X).
范围具有累积分布函数 (Gumbel 1947)
G(吨)=n∫−∞∞F(X)[F(X+吨)−F(X)]n−1 dX
平均范围如下（Hartley and David 1954）：
n∫01F−1[Fn−1−(1−F)n−1]dF
2. 为了n非同分布独立连续随机变量X1,X2,…,Xn具有累积分布函数F1(X),F2(X),…, Fn(X)和概率密度函数F1(X),F2(X),…,Fn(X), 范围具有累积分布函数 (Tsimashenka et al. 2012)
G(吨)=∑一世=1n∫−∞∞F一世(X)∏j=1,j≠一世n[Fj(X+吨)−Fj(X)]dX.
3. 为了n独立同分布的离散随机变量X1,X2,…,Xn具有累积分布函数F(X)和概率质量函数F(X)的范围X一世是大小样本的范围n来自具有分布函数的总体F(X).

$$g(t)=\left{ \begin{array}{l} \sum_{x=1}^{N}[f(x)]^{n} \ \sum_{x=1}^{N-1}\left(\begin{array }{l} {[F(x+t)-F(x-1)]^{n}} \ -[F(x+t)-F(x)]^{n} \ -[F(x +t-1)-F(x-1)]^{n} \ +[F(x+t-1)-F(x)]^{n} \end{数组}\begin{array}{l} \sum_{x=1}^{N}[f(x)]^{n} \ \sum_{x=1}^{N-1}\left(\begin{array }{l} {[F(x+t)-F(x-1)]^{n}} \ -[F(x+t)-F(x)]^{n} \ -[F(x +t-1)-F(x-1)]^{n} \ +[F(x+t-1)-F(x)]^{n} \end{数组}\right) \quad t=0 \end{array} \quad t=1,2,3 \ldots, N-1 .\right.$$

## 金融代写|量化风险管理代写Quantitative Risk Management代考|The Variance

X，表示为和[X], 被定义为勒贝格积分

μ=∫XF(X)dX,

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。