## 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。

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|TFIN101

statistics-lab™ 为您的留学生涯保驾护航 在代写金融数学Intro to Mathematics of Finance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。我们的专家在代写金融数学Intro to Mathematics of Finance代写方面经验极为丰富，各种代写金融数学Intro to Mathematics of Finance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

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Approximations Using Taylor Series

If $f(x)$ is a function which has derivatives of all orders $\left(f^{\prime}, f^{\prime \prime}, f^{\prime \prime \prime}\right.$ etc., all exist) it can be shown that (under certain restrictions) $f(x)$ can be computed as an infinite sum of terms involving its derivatives.
$$f(x)=f(a)+f^{\prime}(a)(x-a)^2+\frac{f^{(2)}(a)}{2 !}(x-a)^2+\cdots+\frac{f^{(n)}(a)}{n !}(x-a)^n+\cdots$$
In the expression above $f^{(n)}(a)$ refers to the $n^{\text {th }}$ derivative of $f$ evaluated at $a$. We can compute approximate values of $f(x)$ near a known value $f(a)$ by using the first few terms in $1.12$.

Example 1.6: Use the first four terms of Equation $1.12$ and $a=0$ to approximate $\sin (x)$
Solution:
\begin{aligned} \sin (x) &=\sin (0)+\sin ^{\prime}(0)(x-0)+\frac{\sin ^{\prime \prime}(0)}{2 !}(x-0)^2+\cdots+\frac{\sin ^{\prime \prime \prime}(0)}{3 !}(x-0)^3 \ &=0+\cos (0)(x-0)+\frac{-\sin (0)}{2 !}(x-0)^2+\frac{-\cos (0)}{3 !}(x-0)^2 \ &=x-\frac{x^3}{6} \end{aligned}
As the sketch below illustrates this approximation is quite good for values of $x$ close to 0 (Figure $1.3$ ).

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Exponents and Logarithms

For convenience we state some of the basic properties of the exponential and logarithmic functions. Unless otherwise stated, we will use the logarithm to base $e$, indicated as $\ln (x)$ and often referred to as the natural logarithm The TI BA II Plus and TI-30XS both have a button devoted to $\ln$ – the 2ND function for this button is $e^x$.
BASIC IDENTITIES
\begin{aligned} \ln (a b) &=\ln (a)+\ln (b) \ \ln \left(a^r\right) &=r \ln (a) \ \ln \left(\frac{a}{b}\right) &=\ln (a)-\ln (b) \ \frac{d \ln (x)}{d x} &=\frac{1}{x}, \quad \frac{d \ln (1+i)}{d i}=\frac{1}{1+i} \ \ln \left(e^x\right) &=e^{\ln (x)}=x \ \frac{d e^x}{d x} &=e^x \ \int e^u d u &=e^u+c \ \int \frac{1}{u} d u &=\ln (|u|)+c \ \int \end{aligned}
Example 1.9: Solve $(1.05)^n=2$.
Solution: We take $\ln$ of both sides to obtain $n \cdot \ln (1.05)=\ln (2)$. Thus, $n=\frac{\ln (2)}{\ln (1.05)} \approx 14.21$.
Example 1.10: Solve for $i$ :
$$(1+i)^3=1+3 \cdot(.05)=1.15 .$$
Solution: We take $\ln$ of both sides to obtain $3 \ln (1+i)=\ln (1.15)$. This gives us $\ln (1+i)=\frac{\ln (1.15)}{3}=0.04658731412$. As a result, $1+i=e^{0.04658731412}=$ 1.047689553. Hence $i=.047686553$. We could also solve this problem by taking the cube root of both sides of the equation. $(1+i)=\sqrt[3]{1.15}=(1.15)^{\frac{1}{3}}=$ $1.047689553$.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Approximations Using Taylor Series

$$f(x)=f(a)+f^{\prime}(a)(x-a)^2+\frac{f^{(2)}(a)}{2 !}(x-a)^2+\cdots+\frac{f^{(n)}(a)}{n !}(x-a)^n+\cdots$$

$$\sin (x)=\sin (0)+\sin ^{\prime}(0)(x-0)+\frac{\sin ^{\prime \prime}(0)}{2 !}(x-0)^2+\cdots+\frac{\sin ^{\prime \prime \prime}(0)}{3 !}(x-0)^3=0+\cos (0)(x$$

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Exponents and Logarithms

$$\ln (a b)=\ln (a)+\ln (b) \ln \left(a^r\right) \quad=r \ln (a) \ln \left(\frac{a}{b}\right)=\ln (a)-\ln (b) \frac{d \ln (x)}{d x} \quad=\frac{1}{x}, \quad \frac{d \ln (1+i)}{d i}$$

$$(1+i)^3=1+3 \cdot(.05)=1.15 .$$

## 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。

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|MATH3090

statistics-lab™ 为您的留学生涯保驾护航 在代写金融数学Intro to Mathematics of Finance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。我们的专家在代写金融数学Intro to Mathematics of Finance代写方面经验极为丰富，各种代写金融数学Intro to Mathematics of Finance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

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Approximation Techniques

In many cases, we will need to solve equations for which no direct method applies. You are probably familiar with the quadratic formula: The solutions to $a x^2+b x+c=0$ are
$$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}$$
There are similar equations for polynomials of degrees 3 and 4 , but no such formula exists for polynomials of degree 5 or higher. In some cases, we can reduce a higher degree polynomial to a quadratic, but these techniques won’t always work. As a result, we will utilize approximating techniques to solve such equations. We will use four methods.
a) Excel’s financial functions.
b) Newton’s Method (not used much anymore, provided as an historical note).
c) MAPLE (very powerful tool, but requires interpretation of results); MAPLE seems little used by financial folk.
d) TI Calculator internal calculation. Along with Excel, this will be the tool you will use most often in “the real world.”

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Newton’s Method

Isaac Newton (1643-1727), an English philosopher and mathematician, did important work in both physics and calculus. His method for approximating roots to polynomials is a very nice application of the tangent line. Joseph Raphson (1648-1715), also English, was made a member of the Royal Society prior to his graduation from Cambridge. See more about these two at the MacTutor History of Mathematics site: http://www-history.mes.standrews.ac.uk/index.html

Newton’s Method solves the equation $f(x)=0$ using an iteration technique. An iteration technique involves three stages:
1) Determining an initial guess (or approximation) called $x_0$,
2) Constructing an algorithm to compute $x_{i+1}$ in terms of $x_i$,
3) A proof that the sequence $x_n$ converges to the required value, in our case a solution of the equation $f(x)=0$.

The process starts with the initial approximation $x_0$ and then computes $x_1$, $x_2$, etc., until a desired degree of accuracy is attained. We will discuss how to make an educated guess (the $x_0$ ) in the context of specific problems ${ }^4$. At this point, we are interested only in describing how Newton’s Method generates the iteration sequence in 2). A proof that the method works is beyond the scope of this text – consult an Advanced Calculus text, if you would like to see a proof.

To create the sequence of approximations using the Newton-Raphson Method, we start with a reasonable first approximation, $x_0$. Often this is done by using a graphing calculator to graph the function and then reading off an estimate from the graph. To find $x_1$, we first construct the tangent line to the graph of $f$ at the point $\left(x_0, f\left(x_0\right)\right)$. The second estimate, $x_1$, is the $x$-intercept of this tangent line.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Approximation Techniques

X=−b±b2−4一个C2一个

a) Excel 的财务功能。
b) 牛顿法（不再使用太多，作为历史记录提供）。
c) MAPLE（非常强大的工具，但需要解释结果）；MAPLE 似乎很少被金融界人士使用。
d) TI 计算器内部计算。与 Excel 一起，这将是您在“现实世界”中最常使用的工具。

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Newton’s Method

1) 确定初始猜测（或近似值），称为X0,
2) 构造一个算法来计算X一世+1按照X一世,
3) 证明该序列Xn收敛到所需的值，在我们的例子中是方程的解F(X)=0.

## 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。

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|ACTL20001

statistics-lab™ 为您的留学生涯保驾护航 在代写金融数学Intro to Mathematics of Finance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。我们的专家在代写金融数学Intro to Mathematics of Finance代写方面经验极为丰富，各种代写金融数学Intro to Mathematics of Finance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

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Sequences and Series

A sequence of payments over time is known as an annuity. We will often need to compute the value of an annuity at a particular point in time. To do so we compute the value of each payment in the sequence (which will depend on the time that payment will be made) and then add those values to obtain the total value. The sequence of sums obtained by adding the terms of a sequence is called a series. For example, if our sequence of terms (payments, usually) is $100,200,300,400$ the series of sums is $100,100+200,100+200+300,100+$ $200+300+400$.

If we compute the sum of the values of the payments at the current time, the result is called the present value (PV) of the annuity. If we compute the accumulated values of the payments at some time in the future, the result is called the future value (FV) of the annuity. In either case, we will usually end up with a geometric series (the sum of a sequence where each term is a constant multiple of the preceding term) and so need the formula for the sum of such a series:
$$\sum_{i=0}^{n-1} a v^i=a+a v+a v^2+\cdots+a v^{n-1}=a \frac{1-v^n}{1-v}$$
Here $a$ is the initial term and $v$ is the common multiple ${ }^1$.
If $|v|<1$ then $\lim {n \rightarrow \infty} v^n=0$ and we can compute the sum of an infinite series of payments (called a perpetuity) as well: $$\sum{i=0}^{\infty} a v^i=\lim _{n \rightarrow \infty} a \frac{1-v^n}{1-v}=\frac{a}{1-v}$$

Using Equations $1.1$ and $1.2$ can be a bit tricky as not all series start at $i=0$. The most direct way to deal with this is to write down a few terms of the series you are dealing with and match them up with Equation $1.1$ or Equation 1.2. Note that you don’t need to figure out the last term since
\begin{aligned} &a=\text { first term } \ &v=\text { common multiple } \ &n=\text { number of terms. } \end{aligned}

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Arithmetic Series

An arithmetic series is created by adding the terms of a sequence where a constant (denoted by $d$ in the formula below) is added to each term to get the next term. In the case of an arithmetic series we have
$$a+(a+d)+(a+2 d)+\cdots+(a+(n-1) d)=\frac{n(2 a+(n-1) d)}{2}$$
Example 1.4: In the simplest case $a=d=1$ and we have the formula Carl Friederich Gauss supposedly proved at age six.
$$\sum_{i=1}^n i=1+2+3+\cdots+n=\frac{n(n+1)}{2}$$
In some cases, we will need to deal with a combination of an arithmetic and a geometric series:
$$A=P v+(P+Q) v^2+(P+2 Q) v^3+\cdots+(P+(n-1) Q) v^n$$
This situation (which we will refer to as a $P-Q$ Series) arises when we have an annuity ${ }^3$ which starts with an initial payment which is then incremented by $Q$ at the end of each subsequent period ( $Q$ can be positive or negative). In many cases $Q$ is added to account for inflation. To simplify this expression we first divide both sides by $v$, obtaining:
$$\frac{A}{v}=P+(P+Q) v+(P+2 Q) v^2+(P+3 Q) v^3+\cdots+(P+(n-1) Q) v^{n-1}$$
Subtracting Equation 1.5 from Equation 1.6 gives us:
$$A\left(\frac{1}{v}-1\right)=A i=P\left(1-v^n\right)+Q\left(v+v^2+v^3+\cdots+v^n\right)-Q n v^n$$

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Sequences and Series

$$\sum_{i=0}^{n-1} a v^i=a+a v+a v^2+\cdots+a v^{n-1}=a \frac{1-v^n}{1-v}$$

$$\sum i=0^{\infty} a v^i=\lim _{n \rightarrow \infty} a \frac{1-v^n}{1-v}=\frac{a}{1-v}$$

$a=$ first term $\quad v=$ common multiple $n=$ number of terms.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Arithmetic Series

$$a+(a+d)+(a+2 d)+\cdots+(a+(n-1) d)=\frac{n(2 a+(n-1) d)}{2}$$

$$\sum_{i=1}^n i=1+2+3+\cdots+n=\frac{n(n+1)}{2}$$

$$A=P v+(P+Q) v^2+(P+2 Q) v^3+\cdots+(P+(n-1) Q) v^n$$

$$\frac{A}{v}=P+(P+Q) v+(P+2 Q) v^2+(P+3 Q) v^3+\cdots+(P+(n-1) Q) v^{n-1}$$

$$A\left(\frac{1}{v}-1\right)=A i=P\left(1-v^n\right)+Q\left(v+v^2+v^3+\cdots+v^n\right)-Q n v^n$$

## 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。

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|MATH3090

statistics-lab™ 为您的留学生涯保驾护航 在代写金融数学Intro to Mathematics of Finance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。我们的专家在代写金融数学Intro to Mathematics of Finance代写方面经验极为丰富，各种代写金融数学Intro to Mathematics of Finance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

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|The Roles of Arbitragers, Hedgers, and Speculators

Hull (2015) discusses three types of traders: ${ }^1$ arbitragers, hedgers, and speculators. Arbitragers, hedgers, and speculators, along with investors, borrowers, and entrepreneurs, all commonly use markets for financial securities and financial derivatives. Understanding the roles of arbitragers, hedgers, and speculators is helpful in understanding why derivatives have emerged and evolved into diverse forms.

## 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。

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|ACTL20001

statistics-lab™ 为您的留学生涯保驾护航 在代写金融数学Intro to Mathematics of Finance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。我们的专家在代写金融数学Intro to Mathematics of Finance代写方面经验极为丰富，各种代写金融数学Intro to Mathematics of Finance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

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|The Role of Financial Assets

Financial assets are the complement to real assets. Financial assets are contractual or indirect claims. Where a real asset directly provides consumption, a financial asset is typically a claim to cash flows and is therefore an indirect claim on consumption. Chapter 2 introduces two major types of financial assets: bonds (as well as other fixed income securities) and stocks.
Bonds and stocks are financial assets. There is one other major and important type of financial asset: financial derivatives. Financial derivatives are financial contracts involving two parties: a buyer or long position, and a seller or short position. Each contract represents a zero-sum game wherein the buyer’s gain is the seller’s loss and vice versa. Finally, the derivative’s cash flows (payoffs) depend on the uncertain price of the contract’s underlying asset at a specified future date.

Accordingly, financial derivatives differ from traditional stocks and bonds in key ways. Financial derivatives are contracts between two (and in a few cases more) parties. The payoff(s) between the parties is derived from (hence the name derivative) or determined by the value of a specified asset that underlies the derivative. For example, an investor who holds bonds of an airline company may enter into a financial derivative with an investment bank that requires the investor to make a series of fixed payments to the bank in return for a promise by the bank that if the airline company defaults on the bonds the bank will make a large cash payment to the company to offset the losses due to the default. In this case, the investor is using a financial derivative to buy financial protection against default from an investment bank.

Financial securities and other financial assets are part of the financial system of a modern economy. Figure $1.1$ illustrates the role of the financial system as a conduit between people and the real assets that meet their needs and desires for consumption.

Financial securities, financial markets, financial institutions, corporations, and even governments are simply concepts in our minds that help organize and structure a society by determining who has the rights to the benefits generated by real assets. Corporations, governments, and other institutions do not produce or consume goods – people do. People are more efficient at producing goods and services, and benefiting from those good and services, when they organize themselves using concepts such as corporations, unions, governments, financial institutions, and so forth. The hallmark of societies with highly successful economies is that they have well-developed financial systems and institutions.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|The Roles of Financial Mathematics and Financial Derivatives

Financial mathematics has provided powerful tools for the development, understanding, and use of the wide spectrum of innovative financial products that have exploded in availability since the 1970s. These financial products have tremendously expanded our abilities to exchange, manage, control, and understand economic risk. Economic risk is intangible and tends to be difficult to understand. Yet it is clear that those economies that develop the greatest skills and tools for dealing with economic risk are best able to harness the incredible power of economic trade and growth to meet the needs and wants of a large society. Financial mathematics lies at the heart of that past success and our ability to create future opportunities.
For example, a large operating firm such as an airline company faces a number of huge economic uncertainties regarding their revenues and expenses. What effects will fuel costs, labor costs, and financing costs have on their profitability and, ultimately, the firm’s ability to continue to provide transportation services? What factors will determine the revenues for forthcoming quarters and years? Will exchange rates and airplane prices change in directions that will prevent the airline company from purchasing new equipment to replace aging aircraft or to open new routes?

Financial derivatives can help the airline company control for risks external to the firm such as changing energy costs, interest rates, and exchange rates. By offsetting or hedging the effects of these otherwise uncontrollable external variables, the company can focus their attention on dealing with those matters over which they have direct control: operating their firm with efficiency, safety, and high-quality service.

Financial derivatives have also played roles in creating or exacerbating financial crises at the international, individual investor, and firm levels. Clearly, derivatives are powerful tools that when used improperly can be as damaging as they are beneficial when used properly.
The key to effective management of financial risk is effective valuation. In finance, valuation of assets in general and financial derivatives in particular involves valuing prospective cash flows based on the timing of those cash flows and their risk. A good definition of finance is that it is the economics of time and risk. This chapter begins with highly simplified examples that ignore the effects of the timing of cash flows and the risk of cash flows on current values. Then the analyses will be expanded to include the time value of money (using forward contracts as an example) and the potential effects of risk on asset values (using options as an example).

## 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。

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|MAT265

statistics-lab™ 为您的留学生涯保驾护航 在代写金融数学Intro to Mathematics of Finance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。我们的专家在代写金融数学Intro to Mathematics of Finance代写方面经验极为丰富，各种代写金融数学Intro to Mathematics of Finance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

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Foundations in Economics and Finance

Financial securities, financial markets, and financial institutions are at the center of the rapid acceleration of economic growth throughout the world economic growth that plays the key role in reducing starvation, increasing life expectancy, expanding educational opportunities, facilitating travel and communication, and generally increasing the choices available to people throughout the world. Even the richest people on earth two centuries ago could not have even imagined the healthcare, transportation, communications, entertainment, and conveniences that are widely available today. Markets, and in particular financial markets, are essential building blocks that have addressed the problems of the past and that will address the challenges of the future.

This first section of Chapter 1 directly addresses the key question as to why it is important that our societies employ substantial numbers of talented employees to develop and operate financial systems. In other words, when a student embarks on a career in finance does he or she become a parasite on society or a vital contributor to the mosaic of talents required to maintain and innovate a modern economy?
The foundation of a modern economic system is capital – resources that have been accumulated in order to facilitate the production of additional resources in the future. The efficient creation, maintenance, and utilization of capital rely on understanding two essential concepts: the time value of money and the management of risk. Financial mathematics centers on facilitating our understanding of the economics of time and risk.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|The Role of Exchanging Real Assets

Real assets are resources that directly enhance our ability to produce and consume goods. Real assets are often viewed as being tangible assets – assets that have physical form such as buildings, land, and equipment. But intangible real assets – assets such as technologies, patents, copyrights, and trademarks are playing an increasingly important role in modern economies.

Without trade, people must make every good that they consume; an incredibly inefficient and ultimately unsustainable system. The ability of people to trade assets is a foundation for an economy. Trade allows people to focus their skills on producing a few products based on their confidence that they can exchange their production for the goods produced by others. When people exchange real assets, they can specialize in producing those goods that best utilize their skills and preferences. More importantly, when people specialize they can discover ways to improve the efficiency of their production – skills which others may adopt. In doing so, the technologies underlying an economy rapidly evolve toward the marvels of today. For example, in the last 150 years, the percentage of the American workforce toiling in agriculture has declined from over $50 \%$ to about $2 \%$, allowing the workforce to provide new and expanded services in areas such as information technology, healthcare, and higher education.

## 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。

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|MATH3090

statistics-lab™ 为您的留学生涯保驾护航 在代写金融数学Intro to Mathematics of Finance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。我们的专家在代写金融数学Intro to Mathematics of Finance代写方面经验极为丰富，各种代写金融数学Intro to Mathematics of Finance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

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|THE RATE OF INTEREST

We begin by considering investments in which capital and interest are paid at the end of a fixed term, there being no intermediate interest or capital payments. This is the simplest form of a cash flow. An example of this kind of investment is a short-term deposit in which the lender invests $£ 1,000$ and receives a return of $£ 1,0356$ months later; $£ 1,000$ may be considered to be a repayment of capital and $£ 35$ a payment of interest, i.e., the reward for the use of the capital for 6 months.

It is essential in any compound interest problem to define the unit of time. This may be, for example, a month or a year, the latter period being frequently used in practice. In certain situations, however, it is more appropriate to choose a different period (e.g., 6 months) as the basic time unit. As we shall see, the choice of time scale often arises naturally from the information one has.
Consider a unit investment (i.e., of 1) for a period of 1 time unit, commencing at time $t$, and suppose that $1+i(t)$ is returned at time $t+1$. We call $i(t)$ the rate of interest for the period $t$ to $t+1$. One sometimes refers to $i(t)$ as the effective rate of interest for the period, to distinguish it from nominal and flat rates of interest, which will be discussed later. If it is assumed that the rate of interest does not depend on the amount invested, the cash returned at time $t+1$ from an investment of $C$ at time $t$ is $C[1+i(t)]$. (Note that in practice a higher rate of interest may be obtained from a large investment than from a small one, but we ignore this point here and throughout this book.)

Recall from Chapter 1 that the defining feature of compound interest is that it is earned on previously earned interest; with this in mind, the accumulation of $C$ from time $t=0$ to time $t=n$ (where $n$ is some positive integer) is
$$C[1+i(0)][1+i(1)] \cdots[1+i(n-1)]$$
This is true since proceeds $C[1+i(0)]$ at time 1 may be invested at this time to produce $C[1+i(0)][1+i(1)]$ at time 2 , and so on.

Rates of interest are often quoted as percentages. For example, we may speak of an effective rate of interest (for a given period) of $12.75 \%$. This means that the effective rate of interest for the period is $0.1275$. As an example, $£ 100$ invested at $12.75 \%$ per annum will accumulate to $£ 100 \times(1+0.1275)=£ 112.75$ after 1 year. Alternatively, $£ 100$ invested at $12.75 \%$ per 2-year period would have accumulated to $£ 112.75$ after 2 years. Computing the equivalent rate of return over different units of time is an essential skill that we will return to later in this chapter.

If the rate of interest per period does not depend on the time $t$ at which the investment is made, we write $i(t)=i$ for all $t$. In this case the accumulation of an investment of $C$ for any period of length $n$ time units is, by Eq. 2.1.1,
$$C(1+i)^n$$
This formula, which will be shown later to hold (under particular assumptions) even when $n$ is not an integer, is referred to as the accumulation of $C$ for $n$ time units under compound interest at rate $i$ per time unit.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|ACCUMULATION FACTORS

As has been implied so far, investments are made in order to exploit the growth of money under the action of compound interest as time goes forward. In order to quantify this growth, we introduce the concept of accumulation factors.
Let time be measured in suitable units (e.g., years); for $t_1 \leq t_2$ we define $A\left(t_1, t_2\right)$ to be the accumulation at time $t_2$ of a unit investment made at time $t_1$ for a term of $\left(t_2-t_1\right)$. It follows by the definition of $i_h(t)$ that, for all $t$ and for all $h>0$, the accumulation over a time unit of length $h$ is
$$A(t, t+h)=1+h i_h(t)$$
and hence that
$$i_h(t)=\frac{A(t, t+h)-1}{h} \quad h>0$$
The quantity $A\left(t_1, t_2\right)$ is often called an accumulation factor, since the accumulation at time $t_2$ of an investment of the sum $C$ at time $t_1$ is
$$C A\left(t_1, t_2\right)$$
We define $A(t, t)=1$ for all $t$, reflecting that the accumulation factor must be unity over zero time.

In relation to the past, i.e., when the present moment is taken as time 0 and $t$ and $t+h$ are both less than or equal to 0 , the factors $A(t, t+h)$ and the nominal rates of interest $i_h(t)$ are a matter of recorded fact in respect of any given transaction. As for their values in the future, estimates must be made (unless one invests in fixed-interest securities with guaranteed rates of interest applying both now and in the future).

Now let $t_0 \leq t_1 \leq t_2$ and consider an investment of 1 at time $t_0$. The proceeds at time $t_2$ will be $A\left(t_0, t_2\right)$ if one invests at time $t_0$ for term $t_2-t_0$, or $A\left(t_0, t_1\right) \times A\left(t_1, t_2\right)$ if one invests at time $t_0$ for term $t_1-t_0$ and then, at time $t_1$, reinvests the proceeds for term $t_2-t_1$. In a consistent market, these proceeds should not depend on the course of action taken by the investor. Accordingly, we say that under the principle of consistency
$$A\left(t_0, t_2\right)=A\left(t_0, t_1\right) A\left(t_1, t_2\right)$$
for all $t_0 \leq t_1 \leq t_2$. It follows easily by induction that, if the principle of consistency holds,
$$A\left(t_0, t_n\right)=A\left(t_0, t_1\right) A\left(t_1, t_2\right) \cdots A\left(t_{n-1}, t_n\right)$$
for any $n$ and any increasing set of numbers $t_0, t_1, \ldots, t_n$.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|THE RATE OF INTEREST

$$C[1+i(0)][1+i(1)] \cdots[1+i(n-1)]$$

$C(1+i)^n$

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|ACCUMULATION FACTORS

$$A(t, t+h)=1+h i_h(t)$$

$$i_h(t)=\frac{A(t, t+h)-1}{h} \quad h>0$$

$$C A\left(t_1, t_2\right)$$

$$A\left(t_0, t_2\right)=A\left(t_0, t_1\right) A\left(t_1, t_2\right)$$

$$A\left(t_0, t_n\right)=A\left(t_0, t_1\right) A\left(t_1, t_2\right) \cdots A\left(t_{n-1}, t_n\right)$$

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## MATLAB代写

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