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

Posted on 2022年12月13日2023年10月17日 by statistics-lab

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|FNCE90082

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.

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 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

我们将主要模拟投资者今天持有未来价值不确定的资产的情况。

我们使用概率概念（随机变量、随机向量、分布、随机过程）和统计工具。特别是，我们假设在概率空间上工作(哦,F,P); 参见 Kolmogorov (1933)。

存在各种类型的风险。我们关注（受监管影响的那些）：
市场风险因基础成分（例如股票/债券/商品价格）变化而导致财务状况损失的风险
信用风险交易对手未能履行其义务（违约）的风险，即未收到承诺的还款（例如贷款/债券）的风险。
操作风险 (OpRisk) 因内部流程、人员和系统不完善或故障或外部事件（例如欺诈、胖手指交易、地震）导致损失的风险。

还有许多其他类型的风险，例如流动性风险、承保风险或模型风险（使用错误指定或不适当的模型来衡量风险的风险；模型风险总是在某种程度上存在）。

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。

金融代写|量化风险管理代写Quantitative Risk Management代考请认准statistics-lab™

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，工具箱允许您学习和应用专业技术。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。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

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

Posted on 2022年11月5日2022年11月5日 by statistics-lab

如果你也在怎样代写金融数学Intro to Mathematics of Finance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。

金融数学是将数学方法应用于金融问题。(有时使用的同等名称是定量金融、金融工程、数学金融和计算金融）。它借鉴了概率、统计、随机过程和经济理论的工具。传统上，投资银行、商业银行、对冲基金、保险公司、公司财务部和监管机构将金融数学的方法应用于诸如衍生证券估值、投资组合结构、风险管理和情景模拟等问题。依赖商品的行业（如能源、制造业）也使用金融数学。定量分析为金融市场和投资过程带来了效率和严谨性，在监管方面也变得越来越重要。

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。

我们提供的金融数学Intro to Mathematics of Finance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

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

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. $(1+i)=\sqrt[3]{1.15}=(1.15)^{\frac{1}{3}}=$ $1.047689553$.

金融数学代考

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

如果 $f(x)$ 是一个具有所有阶导数的函数 $\left(f^{\prime}, f^{\prime \prime}, f^{\prime \prime \prime}\right.$ 等等，都存在) 可以证明（在某些限制下) $f(x)$ 可以计算为涉及其导数的项的无限总和。
$$
f(x)=f(a)+f^{\prime}(a)(x-a)^2+\frac{f^{(2)}(a)}{2 !}(x-a)^2+\cdots+\frac{f^{(n)}(a)}{n !}(x-a)^n+\cdots
$$
在上面的表达式中 $f^{(n)}(a)$ 指的是 $n^{\text {th }}$ 的导数 $f$ 评价为 $a$. 我们可以计算近似值 $f(x)$ 接近已知值 $f(a)$ 通过使用前几个术语 $1.12$.
例 1.6：使用公式的前四项 $1.12$ 和 $a=0$ 近似 $\sin (x)$
解决方案:
$$
\sin (x)=\sin (0)+\sin ^{\prime}(0)(x-0)+\frac{\sin ^{\prime \prime}(0)}{2 !}(x-0)^2+\cdots+\frac{\sin ^{\prime \prime \prime}(0)}{3 !}(x-0)^3=0+\cos (0)(x
$$
正如下面的草图所示，这个近似值对于 $x$ 接近于 0 (图 $1.3$ ).

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

为方便起见，我们陈述了指数函数和对数函数的一些基本性质。除非另有说明，否则我们将以对数为底 $e$ ，表示为 $\ln (x)$ 并且通常被称为自然对数 TI BA II Plus 和 TI-30XS 都有一个专门用于ln- 此按钮的 2ND 功能是 $e^x$. 基本身份
$$
\ln (a b)=\ln (a)+\ln (b) \ln \left(a^r\right) \quad=r \ln (a) \ln \left(\frac{a}{b}\right)=\ln (a)-\ln (b) \frac{d \ln (x)}{d x} \quad=\frac{1}{x}, \quad \frac{d \ln (1+i)}{d i}
$$
例 1.9: 求解 $(1.05)^n=2$.
解决方案: 我们采取ln双方获得 $n \cdot \ln (1.05)=\ln (2)$. 因此， $n=\frac{\ln (2)}{\ln (1.05)} \approx 14.21$.
例 1.10: 求解 $i$ :
$$
(1+i)^3=1+3 \cdot(.05)=1.15 .
$$
解决方案: 我们采取 $\ln$ 双方获得 $3 \ln (1+i)=\ln (1.15)$. 这给了我们 $\ln (1+i)=\frac{\ln (1.15)}{3}=0.04658731412$. 因此， $1+i=e^{0.04658731412}=1.047689553$ 。因此 $i=.047686553$. 我们也可以通过对等式两边取立方根来解决这个问题。 $(1+i)=\sqrt[3]{1.15}=(1.15)^{\frac{1}{3}}=$ $1.047689553$.

数学代写|金融数学代写Intro to Mathematics of Finance代考请认准statistics-lab™

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

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。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

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

Posted on 2022年11月5日2022年11月5日 by statistics-lab

如果你也在怎样代写金融数学Intro to Mathematics of Finance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。

我们提供的金融数学Intro to Mathematics of Finance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

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|MATH3090

金融数学代考

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

在许多情况下，我们需要求解没有直接方法适用的方程。您可能熟悉二次公式：一个X2+bX+C=0是

X=−b±b2−4一个C2一个
对于 3 次和 4 次多项式有类似的方程，但对于 5 次或更高次的多项式不存在这样的公式。在某些情况下，我们可以将更高次多项式简化为二次，但这些技术并不总是有效。因此，我们将利用近似技术来求解这些方程。我们将使用四种方法。
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

英国哲学家和数学家艾萨克·牛顿（Isaac Newton，1643-1727）在物理学和微积分方面都做出了重要贡献。他将根近似为多项式的方法是切线的一个很好的应用。Joseph Raphson (1648-1715) 也是英国人，在他从剑桥大学毕业之前就成为了英国皇家学会的成员。在 MacTutor 数学史网站上查看更多关于这两个的信息：http://www-history.mes.standrews.ac.uk/index.html

牛顿法求解方程F(X)=0使用迭代技术。迭代技术涉及三个阶段：
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.

该过程从初始近似值开始X0然后计算X1, X2等，直到达到所需的准确度。我们将讨论如何做出有根据的猜测（X0) 在具体问题的背景下4. 此时，我们只对描述牛顿法如何生成 2) 中的迭代序列感兴趣。该方法有效的证明超出了本文的范围——如果您想查看证明，请参阅高级微积分文本。

为了使用 Newton-Raphson 方法创建近似序列，我们从一个合理的第一近似开始，X0. 通常这是通过使用图形计算器绘制函数图，然后从图中读取估计值来完成的。寻找X1，我们首先构造图的切线F在这一点上(X0,F(X0)). 第二个估计，X1，是个X-这条切线的截距。

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

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。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

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

Posted on 2022年11月5日2022年11月5日 by statistics-lab

如果你也在怎样代写金融数学Intro to Mathematics of Finance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。

我们提供的金融数学Intro to Mathematics of Finance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

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

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

金融数学代考

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

随着时间的推移，一系列付款被称为年金。我们经常需要计算特定时间点的年金价值。为此，我们计算序列中每笔付款的价值（这将取决于付款的时间），然后将这些值相加以获得总价值。将数列的各项相加得到的和的数列称为数列。例如，如果我们的条款序列（通常是付款）是 $100,200,300,400$ 总和系列是 $100,100+200,100+200+300,100+200+300+400$.
如果我们计算当前时间的付款值的总和，则结果称为年金的现值 (PV) 。如果我们计算末来某个时间支付的累计值，则结果称为年金的末来值 (FV) 。在任何一种情况下，我们通常都会得到一个几何级数（一个序列的总和，其中每一项都是前一项的常数倍数），因此需要这个数列总和的公式:
$$
\sum_{i=0}^{n-1} a v^i=a+a v+a v^2+\cdots+a v^{n-1}=a \frac{1-v^n}{1-v}
$$
这里 $a$ 是初始项，并且 $v$ 是公倍数 ${ }^1$.
如果 $|v|<1$ 然后 $\lim n \rightarrow \infty v^n=0$ 我们还可以计算无限系列支付的总和（称为永续年金)：
$$
\sum i=0^{\infty} a v^i=\lim _{n \rightarrow \infty} a \frac{1-v^n}{1-v}=\frac{a}{1-v}
$$
使用方程式 $1.1$ 和 $1.2$ 可能有点棘手，因为并非所有系列都从 $i=0$. 解决这个问题的最直接方法是写下您正在处理的系列的一些术语，并将它们与方程式匹配1.1或公式 1.2。请注意，您不需要计算上一个术语，因为
$a=$ 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

算术级数是通过添加一个序列的项来创建的，其中一个常数（表示为 $d$ 在下面的公式中）被添加到每个术语以获得下一个术语。在算术级数的情况下，我们有
$$
a+(a+d)+(a+2 d)+\cdots+(a+(n-1) d)=\frac{n(2 a+(n-1) d)}{2}
$$
示例 1.4：在最简单的情况下 $a=d=1$ 我们有卡尔弗里德里希高斯据说在六岁时证明的公式。
$$
\sum_{i=1}^n i=1+2+3+\cdots+n=\frac{n(n+1)}{2}
$$
在某些情况下，我们需要处理算术级数和几何级数的组合:
$$
A=P v+(P+Q) v^2+(P+2 Q) v^3+\cdots+(P+(n-1) Q) v^n
$$
这种情况（我们将其称为 $P-Q$ Series) 在我们有年金时出现 ${ }^3$ 从初始付款开始，然后增加 $Q$ 在每个后续期间结束时 ( $Q$ 可以是正面的也可以是负面的) 。在很多情况下 $Q$ 被添加以解释通货膨胀。为了简化这个表达式，我们首先将两边除以 $v$ ，获得:
$$
\frac{A}{v}=P+(P+Q) v+(P+2 Q) v^2+(P+3 Q) v^3+\cdots+(P+(n-1) Q) v^{n-1}
$$
从公式 $1.6$ 中减去公式 $1.5$ 得出:
$$
A\left(\frac{1}{v}-1\right)=A i=P\left(1-v^n\right)+Q\left(v+v^2+v^3+\cdots+v^n\right)-Q n v^n
$$

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

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。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

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

Posted on 2022年11月4日2022年11月4日 by statistics-lab

如果你也在怎样代写金融数学Intro to Mathematics of Finance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。

我们提供的金融数学Intro to Mathematics of Finance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

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.

An important concept before discussing these roles is short selling. The idea that a trader can take a short position in a financial derivative was introduced. It makes sense that, as a contract between two people regarding the price of an asset one of the parties to the contract will take the long side and one will take the short side. Having the long side of the contract means that one will have the risk exposure more similar to owning the asset with the other side having an exposure similar to owing the asset. Short selling is the process of obtaining the opposite exposure of owing an asset by borrowing the asset and selling it into the market at the current market price. The short seller of an asset therefore is inversely exposed to the price changes of the underlying asset: the short seller gains if the underlying stock or other asset’s market price falls and loses market value if the asset rises in value. Eventually, the short seller purchases the asset and returns it Io the entity from which it was borrowed, terminating the short sale. Ignoring dividends and the time value of money, the short seller of a stock the stuck rises by $\$ X$.

Arbitragers are traders who establish a long (or buy) position in one or more assets that they believe are relatively underpriced and one or more short (or sell) positions in assets that they believe are relatively overpriced. Arbitragers hold these positions based on their belief that the prices will revert to more proper price levels that allow the arbitrager to exit both positions at a net profit. When markets are poorly or inefficiently priced, arbitragers can earn riskless or virtually riskless profits. Successful arbitragers serve the market by correcting pricing errors thereby (and unintentionally) ensuring that less informed market participants are transacting at prices that are nearer to their proper or equilibrium values. The distinguishing feature of arbitragers is that their trades are designed to take very little risk and tend to be short term.

Hedgers are market participants that use financial derivatives and other instruments to offset risks that they do not wish to bear. For example, an agricultural firm may use derivatives to lock in the revenues from their output such as food products, lock down their costs of production such as energy costs, and minimize their exposure to exchange rates from their contracts to export their products. Financial derivatives allow hedgers to hedge or “lay off” those risks that they cannot control and allow them to focus on those factors over which they may have control.

Speculators are similar to arbitragers except that they typically take substantially more risk by establishing one or more positions with unhedged risks. Speculators take positions in anticipation of profits if their forecasts of future price movements are accurate. The key to successful speculators is that they gain money and are able to continue speculating only when they are able to consistently buy assets that are underpriced and sell assets that are consistently overpriced. In doing do, they can consistently earn profits while acting to balance supply and demand, drive prices toward their true values, and stabilize markets and prices.

数学代写|金融数学代写Intro to Mathematics of Finance代考|Market Prices, Risk, and Randomness

Risk is a fascinating topic that is central to financial economics. What causes risk, and what causes security prices to change? The answers to these questions and the study of financial risk in general have progressed primarily using financial math.

The terms value and price (as well as the terms valuation and pricing) are often used interchangeably in finance. This book tends to use the term value to describe how much a particular person believes an item is worth and uses the term price to describe the amount of money that people receive or pay when they exchange the item. However, the term asset pricing is used frequently in financial economics to describe very important models even when the context is more clearly described as involving asset valuation.

Since the general meaning of the terms are quite similar, this book often uses the terms price and pricing to describe values and valuation in cases where price and pricing are conventionally used.

The value of an asset tends to change through time because the preferences of people change through time and the abilities of a modern economy to meet those preferences changes through time. Agricultural prices change due to factors such as weather, energy prices change due to factors such as economic activity, and stock prices change due to factors such as predictions of future revenues and expenses. Prices respond to changes as soon as the information about those changes is revealed. The effects of a frost on orange harvests begin changing market prices of oris done.

The spot price is the price today for delivery today. The spot price of an asset such as a stock or bond reflects a consensus in the marketplace with regard to the future benefits that the asset offers. As time passes, the asset price changes because the market’s predictions of future conditions change. More generally, asset prices change because of the arrival of new information. Good news for a stock such as higher forecasts of earnings causes a positive price change, while bad news such as a disappointment regarding the sales of a new product causes a negative price change. To the extent that market participants rationally and efficiently process available information to form the current price of an asset, it follows based on the arrival of new information.
Therefore, security prices can be viewed as random variables that change through time based on the arrival of new information. Simply put, the future price of an asset can be modeled as being equal to its future expected value plus or minus price changes due to new information that becomes available to market participants.

金融数学代考

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) 讨论了三种类型的交易者：1套利者、套期保值者和投机者。套利者、套期保值者和投机者，以及投资者、借款者和企业家，通常都使用金融证券和金融衍生品市场。了解套利者、套期保值者和投机者的角色有助于理解为什么衍生品会出现并演变成多种形式。

在讨论这些角色之前，一个重要的概念是卖空。引入了交易者可以在金融衍生品中做空头寸的想法。有意义的是，作为两个人之间关于资产价格的合同，合同的一方将采取多头一方，另一方将采取空方。拥有合约的多头意味着一方的风险敞口与拥有资产更相似，而另一方的风险敞口类似于欠资产。卖空是通过借入资产并以当前市场价格将其出售到市场来获得所欠资产的相反风险敞口的过程。因此，资产的卖空者反向暴露于标的资产的价格变化：如果标的股票或其他资产的市场价格下跌，卖空者就会获利，如果资产价值上涨，卖空者就会失去市场价值。最终，卖空者购买资产并将其归还给借入资产的实体，从而终止卖空。忽略股息和货币时间价值，被困股票的卖空者上涨$X.

套利者是在他们认为相对低估的一种或多种资产中建立多头（或买入）头寸并在他们认为相对高估的资产中建立一个或多种空头（或卖出）头寸的交易者。套利者持有这些头寸是因为他们相信价格将恢复到更合适的价格水平，从而允许套利者以净利润退出两个头寸。当市场定价不佳或效率低下时，套利者可以获得无风险或几乎无风险的利润。成功的套利者通过纠正定价错误来为市场服务，从而（并且无意中）确保信息较少的市场参与者以更接近其适当或均衡价值的价格进行交易。

对冲者是使用金融衍生品和其他工具来抵消他们不想承担的风险的市场参与者。例如，一家农业公司可以使用衍生品来锁定其产出（如食品）的收入，锁定其生产成本（如能源成本），并尽量减少其产品出口合同中的汇率风险。金融衍生品允许套期保值者对冲或“放弃”他们无法控制的风险，并允许他们专注于他们可能控制的那些因素。

投机者与套利者相似，只是他们通常通过建立一个或多个未对冲风险的头寸来承担更大的风险。如果投机者对未来价格走势的预测准确，他们就会在预期利润的情况下建仓。成功的投机者的关键是他们赚钱，并且只有当他们能够持续购买被低估的资产并出售一直被高估的资产时，他们才能继续投机。在这样做的过程中，他们可以在平衡供需、推动价格接近其真实价值、稳定市场和价格的同时持续赚取利润。

数学代写|金融数学代写Intro to Mathematics of Finance代考|Market Prices, Risk, and Randomness

风险是一个引人入胜的话题，是金融经济学的核心。是什么导致了风险，又是什么导致了证券价格的变化？这些问题的答案和一般金融风险的研究主要使用金融数学取得了进展。

术语价值和价格（以及术语估值和定价）在金融中经常互换使用。这本书倾向于使用价值这个词来描述一个特定的人认为一件物品的价值，并使用价格这个词来描述人们在交换物品时收到或支付的金额。然而，资产定价一词在金融经济学中经常用于描述非常重要的模型，即使上下文被更清楚地描述为涉及资产估值。

由于这些术语的一般含义非常相似，因此本书经常使用术语价格和定价来描述通常使用价格和定价的情况下的价值和估值。

资产的价值往往会随着时间而变化，因为人们的偏好会随着时间而变化，而现代经济满足这些偏好的能力也会随着时间而变化。农产品价格因天气等因素而变化，能源价格因经济活动等因素而变化，股票价格因未来收入和支出预测等因素而变化。一旦有关这些变化的信息被披露，价格就会对变化做出反应。霜冻对橙子收成的影响开始改变 oris done 的市场价格。

现货价格是今天交割的价格。股票或债券等资产的现货价格反映了市场对资产提供的未来收益的共识。随着时间的推移，资产价格会发生变化，因为市场对未来状况的预测会发生变化。更一般地说，资产价格会随着新信息的到来而发生变化。对股票的好消息（例如更高的收益预测）会导致价格上涨，而坏消息（例如对新产品销售的失望）会导致价格下跌。只要市场参与者合理有效地处理可用信息以形成资产的当前价格，它就会基于新信息的到来而遵循。
因此，证券价格可以被视为随机变量，随着新信息的到来而随时间变化。简而言之，资产的未来价格可以建模为等于其未来预期价值加上或减去市场参与者可获得的新信息导致的价格变化。

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

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。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

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

Posted on 2022年11月4日2022年11月4日 by statistics-lab

如果你也在怎样代写金融数学Intro to Mathematics of Finance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。

我们提供的金融数学Intro to Mathematics of Finance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

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).

金融数学代考

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

金融资产是实物资产的补充。金融资产是合同或间接债权。在实物资产直接提供消费的情况下，金融资产通常是对现金流的债权，因此是对消费的间接债权。第 2 章介绍了两种主要类型的金融资产：债券（以及其他固定收益证券）和股票。
债券和股票是金融资产。还有另一种主要且重要的金融资产类型：金融衍生品。金融衍生品是涉及两方的金融合约：买方或多头头寸，以及卖方或空头头寸。每份合约都代表一个零和游戏，其中买方的收益是卖方的损失，反之亦然。最后，衍生品的现金流（收益）取决于合约标的资产在特定未来日期的不确定价格。

因此，金融衍生品在关键方面不同于传统的股票和债券。金融衍生品是两方（在少数情况下甚至更多）之间的合同。各方之间的收益来自（因此称为衍生品）或由衍生品所依据的特定资产的价值确定。例如，持有航空公司债券的投资者可能与投资银行签订金融衍生品，要求投资者向银行支付一系列固定款项，以换取银行承诺如果航空公司违约对于债券，银行将向公司支付大笔现金，以弥补违约造成的损失。在这种情况下，投资者使用金融衍生品从投资银行购买金融保护以防止违约。

金融证券和其他金融资产是现代经济金融体系的一部分。数字1.1说明了金融系统作为人们与满足其消费需求和愿望的实物资产之间的管道的作用。

金融证券、金融市场、金融机构、公司甚至政府只是我们头脑中的概念，它们通过确定谁有权获得实物资产产生的利益来帮助组织和构建一个社会。公司、政府和其他机构不生产或消费商品——人们会。当人们使用诸如公司、工会、政府、金融机构等概念组织起来时，人们在生产商品和服务并从这些商品和服务中受益时会更有效率。经济高度成功的社会的标志是它们拥有发达的金融体系和机构。

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

金融数学为开发、理解和使用自 1970 年代以来广泛使用的创新金融产品提供了强大的工具。这些金融产品极大地扩展了我们交换、管理、控制和理解经济风险的能力。经济风险是无形的，往往难以理解。然而很明显，那些发展出最强大的技能和工具来应对经济风险的经济体最有能力利用经济贸易和增长的强大力量来满足大社会的需求。金融数学是过去成功的核心，也是我们创造未来机会的能力的核心。
例如，航空公司等大型运营公司在收入和支出方面面临许多巨大的经济不确定性。燃料成本、劳动力成本和融资成本对其盈利能力以及最终对公司继续提供运输服务的能力有何影响？哪些因素将决定未来季度和年度的收入？汇率和飞机价格的变化是否会阻止航空公司购买新设备来更换老化的飞机或开辟新航线？

金融衍生品可以帮助航空公司控制公司外部的风险，例如不断变化的能源成本、利率和汇率。通过抵消或对冲这些无法控制的外部变量的影响，公司可以将注意力集中在处理他们可以直接控制的事项上：以高效、安全和高质量的服务运营公司。

金融衍生品也在国际、个人投资者和公司层面造成或加剧金融危机方面发挥了作用。显然，衍生工具是强大的工具，如果使用不当，它们的破坏性可能与正确使用时的益处一样大。
有效管理财务风险的关键是有效估值。在金融领域，一般资产和金融衍生品的估值涉及根据这些现金流的时间及其风险对预期现金流进行估值。金融的一个很好的定义是它是时间和风险的经济学。本章从高度简化的示例开始，这些示例忽略了现金流时间的影响和现金流对当前价值的风险。然后将分析扩展到包括货币时间价值（以远期合约为例）和风险对资产价值的潜在影响（以期权为例）。

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

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。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

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

Posted on 2022年11月4日2022年11月4日 by statistics-lab

如果你也在怎样代写金融数学Intro to Mathematics of Finance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。

我们提供的金融数学Intro to Mathematics of Finance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

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

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.

金融数学代考

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

金融证券、金融市场和金融机构处于全球经济快速增长的中心，经济增长在减少饥饿、延长预期寿命、扩大教育机会、促进旅行和交流以及普遍增加经济增长方面发挥着关键作用可供全世界人民使用的选择。即使是两个世纪前地球上最富有的人，也无法想象今天广泛使用的医疗保健、交通、通讯、娱乐和便利设施。市场，尤其是金融市场，是解决过去问题并将应对未来挑战的重要组成部分。

第一章的第一部分直接解决了一个关键问题，即为什么我们的社会雇佣大量有才能的员工来开发和运营金融系统很重要。换句话说，当一个学生开始从事金融职业时，他或她是成为社会的寄生虫，还是成为维持和创新现代经济所需的大量人才的重要贡献者？
现代经济体系的基础是资本——为促进未来额外资源的生产而积累的资源。资本的有效创造、维护和利用依赖于对两个基本概念的理解：货币的时间价值和风险管理。金融数学的中心是促进我们对时间和风险经济学的理解。

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

实物资产是直接增强我们生产和消费商品能力的资源。实物资产通常被视为有形资产——具有物理形式的资产，例如建筑物、土地和设备。但无形的实物资产——技术、专利、版权和商标等资产在现代经济中发挥着越来越重要的作用。

没有贸易，人们必须制造他们消费的每一件商品；一个极其低效且最终不可持续的系统。人们交易资产的能力是经济的基础。贸易使人们能够将他们的技能集中在生产一些产品上，因为他们相信他们可以用自己的产品换取其他人生产的商品。当人们交换实物资产时，他们可以专门生产最能利用他们的技能和偏好的商品。更重要的是，当人们专业化时，他们可以找到提高生产效率的方法——其他人可能会采用的技能。在这样做的过程中，支撑经济的技术迅速朝着今天的奇迹发展。例如，在过去的 150 年中，从事农业劳动的美国劳动力的百分比从超过50%大概2%，允许劳动力在信息技术、医疗保健和高等教育等领域提供新的和扩展的服务。

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

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。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

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

Posted on 2022年10月31日2022年10月31日 by statistics-lab

如果你也在怎样代写金融数学Intro to Mathematics of Finance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。

我们提供的金融数学Intro to Mathematics of Finance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

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 $t_0, t_1, \ldots, t_n$.

金融数学代考

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

我们首先考虑在固定期限结束时支付资本和利息的投资，没有中间利息或资本支付。这是最简单的现金流形式。这种投资的一个例子是贷方投资的短期存款 $£ 1,000$ 并收到回报 $£ 1,0356$ 几个月后; $£ 1,000$ 可被视为资本偿还，并且 $£ 35$ 支付利息，即使用资金6个月的奖励。
在任何复利问题中，定义时间单位都是必不可少的。例如，这可能是一个月或一年，后者在实践中经常使用。然而，在某些情况下，选择不同的时期（例如，6个月）作为基本时间单位更为合适。正如我们将看到的，时间尺度的选择通常是从人们所拥有的信息中自然产生的。
考虑一个单位投资（即 1 个）持续 1 个时间单位，从时间开始 $t$ ，并假设 $1+i(t)$ 在时间返回 $t+1$. 我们称之为 $i(t)$ 该期间的利率 $t$ 至 $t+1$. 一有时指 $i(t)$ 作为该期间的实际利率，将其与名义利率和固定利率区分开来，这将在后面讨论。如果假设利率不取决于投入的金额，则按时返还的现金 $t+1$ 从投资 $C$ 有时 $t$ 是 $C[1+i(t)]$.（请注意，在实践中，大笔投资可能比小笔投资获得更高的利率，但我们在此处和整本书中都忽略了这一点。）
回想一下第 1 章，复利的定义特征是它是在以前赚取的利息上赚取的；考虑到这一点，积㽧 $C$ 从时间 $t=0$ 到时间 $t=n$ (在哪哩 $n$ 是某个正整数) 是
$$
C[1+i(0)][1+i(1)] \cdots[1+i(n-1)]
$$
这是真的，因为收益 $C[1+i(0)]$ 在时间 1 可以在此时投资以生产 $C[1+i(0)][1+i(1)]$ 在时间 2 ，依此类推。
利率通常以百分比表示。例如，我们可以说有效利率 (对于给定时期) $12.75 \%$. 这意味着该期间的实际利率为 $0.1275$. 举个例子， $£ 100$ 投资于 $12.75 \%$ 每年将㽧积到 $100 \times(1+0.1275)=£ 112.751$ 年后。或者， $£ 100$ 投资于 $12.75 \%$ 每 2 年期间将累积到£ $112.752$ 年后。计算不同时间单位的等效收益率是一项基本技能，我们将在本章后面讨论。
如果每期利率不取决于时间 $t$ 在哪里进行投资，我们写 $i(t)=i$ 对所有人 $t$. 在这种情况下，投资的积㽧 $C$ 对于任何长度的时期 $n$ 时间单位是，由等式。2.1.1，
$C(1+i)^n$
这个公式，稍后将显示 (在特定假设下) 即使当 $n$ 不是整数，称为㽧加 $C$ 为了 $n$ 复利下的时间单位 $i$ 每个时间单位。

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

正如迄今为止所暗示的那样，随着时间的推移，进行投资是为了在复利的作用下利用货币的增长。为了量化这种增长，我们引入了㽧积因子的概念。
让时间以适当的单位 (例如，年) 来衡量; 为了 $t_1 \leq t_2$ 我们定义 $A\left(t_1, t_2\right)$ 成为时间的积累 $t_2$ 一次进行的单位投资 $t_1$ 任期 $\left(t_2-t_1\right)$. 它遵偱以下定义 $i_h(t)$ 那，对于所有人 $t$ 并为所有人 $h>0$ ，在一个时间单位长度上的累积 $h$ 是
$$
A(t, t+h)=1+h i_h(t)
$$
因此
$$
i_h(t)=\frac{A(t, t+h)-1}{h} \quad h>0
$$
数量 $A\left(t_1, t_2\right)$ 通常被称为累积因子，因为时间累积 $t_2$ 投资总额 $C$ 有时 $t_1$ 是
$$
C A\left(t_1, t_2\right)
$$
我们定义 $A(t, t)=1$ 对所有人 $t$ ，反映累积因子在零时间内必须是统一的。
相对于过去，即当现在时刻被视为时间 0 和 $t$ 和 $t+h$ 都小于或等于 0 ，因子 $A(t, t+h)$ 和名义利率 $i_h(t)$ 是任何特定交易的记录事实。至于它们在末来的价值，必须进行估计（除非投资于现在和末来都适用的保证利率的固定利率证券) 。
现在让 $t_0 \leq t_1 \leq t_2$ 并考虑一次投资 $1 t_0$. 当时的收益 $t_2$ 将佘 $A\left(t_0, t_2\right)$ 如果一个人在时间投资 $t_0$ 任期 $t_2-t_0$ ，或者 $A\left(t_0, t_1\right) \times A\left(t_1, t_2\right)$ 如果一个人在时间投资 $t_0$ 任期 $t_1-t_0$ 然后，有时 $t_1$ ，将收益再投资期限 $t_2-t_1$. 在一致的市场中，这些收益不应取决于投资者采取的行动。因此，我们说在一致性原则下
$$
A\left(t_0, t_2\right)=A\left(t_0, t_1\right) A\left(t_1, t_2\right)
$$
对所有人 $t_0 \leq t_1 \leq t_2$. 通过归纳很容易得出，如果一致性原则成立，
$$
A\left(t_0, t_n\right)=A\left(t_0, t_1\right) A\left(t_1, t_2\right) \cdots A\left(t_{n-1}, t_n\right)
$$
对于任何 $n$ 和任何增加的数字集 $t_0, t_1, \ldots, t_n$.

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

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。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

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

Posted on 2022年10月31日2022年10月31日 by statistics-lab

如果你也在怎样代写金融数学Intro to Mathematics of Finance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。

我们提供的金融数学Intro to Mathematics of Finance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

数学代写|金融数学代写Intro to Mathematics of Finance代考|COMPOUND INTEREST

Suppose now that a certain type of savings account pays simple interest at the rate of $i$ per annum. Suppose further that this rate is guaranteed to apply throughout the next 2 years and that accounts may be opened and closed at any time. Consider an investor who opens an account at the present time $(t=0)$ with an initial deposit of $C$. The investor may close this account after 1 year $(t=1)$, at which time he will withdraw $C(1+i)$ (see Eq. 1.2.1). He may then place this sum on deposit in a new account and close this second account after one further year $(t=2)$. When this latter account is closed, the sum withdrawn (again see Eq. 1.2.1) will be
$$
[C(1+i)] \times(1+i)=C(1+i)^2=C\left(1+2 i+i^2\right)
$$
If, however, the investor chooses not to switch accounts after 1 year and leaves his money in the original account, on closing this account after 2 years, he will receive $C(1+2 i)$. Therefore, simply by switching accounts in the middle of the 2-year period, the investor will receive an additional amount $i^2 C$ at the end of the period. This extra payment is, of course, equal to $i(i C)$ and arises as interest paid (at $t=2$ ) on the interest credited to the original account at the end of the first year.
From a practical viewpoint, it would be difficult to prevent an investor switching accounts in the manner described here (or with even greater frequency). Furthermore, the investor, having closed his second account after 1 year, could then deposit the entire amount withdrawn in yet another account. Any bank would find it administratively very inconvenient to have to keep opening and closing accounts in the manner just described. Moreover, on closing one account, the investor might choose to deposit his money elsewhere. Therefore, partly to encourage long-term investment and partly for other practical reasons, it is common commercial practice (at least in relation to investments of duration greater than 1 year) to pay compound interest on savings accounts. Moreover, the concepts of compound interest are used in the assessment and evaluation of investments as discussed throughout this book.

The essential feature of compound interest is that interest itself earns interest. The operation of compound interest may be described as follows: consider a savings account, which pays compound interest at rate $i$ per annum, into which is placed an initial deposit $C$ at time $t=0$. (We assume that there are no further payments to or from the account.) If the account is closed after 1 year ( $\mathrm{t}=1)$ the investor will receive $C(1+\mathrm{i})$. More generally, let $A_n$ be the amount that will be received by the investor if he closes the account after $n$ years $(\mathrm{t}=\mathrm{n})$.

数学代写|金融数学代写Intro to Mathematics of Finance代考|SOME PRACTICAL ILLUSTRATIONS

As a simple illustration, consider an investor who is offered a contract with a financial institution that provides $£ 22,500$ at the end of 10 years in return for a single payment of $£ 10,000$ now. If the investor is willing to tie up this amount of capital for 10 years, the decision as to whether or not he enters into the contract will depend upon the alternative investments available. For example, if the investor can obtain elsewhere a guaranteed compound rate of interest for the next 10 years of $10 \%$ per annum, then he should not enter into the contract as, from Eq. 1.3.3, £10,000 $\times(1+10 \%)^{10}=£ 25,937.42$, which is greater than $£ 22,500$.

However, if he can obtain this rate of interest with certainty only for the next 6 years, in deciding whether or not to enter into the contract, he will have to make a judgment about the rates of interest he is likely to be able to obtain over the 4-year period commencing 6 years from now. (Note that in these illustrations we ignore further possible complications, such as the effect of taxation or the reliability of the company offering the contract.)

Similar considerations would apply in relation to a contract which offered to provide a specified lump sum at the end of a given period in return for the payment of a series of premiums of stated (and often constant) amount at regular intervals throughout the period. Would an investor favorably consider a contract that provides $£ 3,500$ tax free at the end of 10 years in return for ten annual premiums, each of $£ 200$, payable at the start of each year? This question can be answered by considering the growth of each individual premium to the end of as, from Eq. 1.3.3, £10,000 $\times(1+10 \%)^{10}=£ 25,937.42$, which is greater than $£ 22,500$.

Similar considerations would apply in relation to a contract which offered to provide a specified lump sum at the end of a given period in return for the payment of a series of premiums of stated (and often constant) amount at regular intervals throughout the period. Would an investor favorably consider a contract that provides $£ 3,500$ tax free at the end of 10 years in return for ten annual premiums, each of $£ 200$, payable at the start of each year? This question can be answered by considering the growth of each individual premium to the end of the 10-year term under a particular rate of compound interest available to him elsewhere and comparing the resulting value to $£ 3,500$. However, a more elegant approach is related to the concept of annuities as introduced in Chapter 3.

金融数学代考

数学代写|金融数学代写Intro to Mathematics of Finance代考|COMPOUND INTEREST

现在假设某种类型的储蓄账户支付单利，利率为 $i$ 每年。进一步假设该利率保证在末来 2 年内适用，并且可以随时开设和关闭账户。考虑一个目前开户的投资者 $(t=0)$ 初始存款为 $C$. 投资者可在 1 年后关闭此账户 $(t=1) ，$ 此时他将退出 $C(1+i)$ （见公式 1.2.1) 。然后，他可以将这笔款项存入一个新账户，并在一年后关闭第二个账户 $(t=2)$. 当后一个账户关闭时，提取的金额 (再次参见公式 1.2.1) 将为
$$
[C(1+i)] \times(1+i)=C(1+i)^2=C\left(1+2 i+i^2\right)
$$
但是，如果投资者选择在 1 年后不切换账户并将其资金留在原账户中，则在 2 年后关闭该账户时，他将收到 $C(1+2 i)$. 因此，只需在 2 年的中间转换账户，投资者将获得额外的金额 $i^2 C$ 在期末。当然，这笔额外费用等于 $i(i C)$ 并作为支付的利息产生 $($ 在 $t=2)$ 在第一年末记入原始帐户的利息。
从实际的角度来看，很难阻止投资者以此处描述的方式 (或以更高的频率) 转换账户。此外，投资者在 1 年后关闭了他的第二个账户，然后可以将提取的全部金额存入另一个账户。任何银行都会发现必须以刚才描述的方式开立和关闭账户在管理上非常不便。此外，在关闭一个账户时，投资者可能会选择将资金存入其他地方。因此，部分是为了鼓励长期投资，部分是出于其他实际原因，为储蓄账户支付复利是常见的商业愢例（至少对于期限超过 1 年的投资而言）。而且，
复利的本质特征是利息本身就会产生利息。复利的操作可以描述如下：考虑一个储㦎账户，它按利率支付复利 $i$ 每年，其中存入初始存款 $C$ 有时 $t=0$. (我们假设该帐户没有进一步的付款。) 如果帐户在 1 年后关闭 $(\mathrm{t}=1$ )投资者将获得 $C(1+\mathrm{i})$. 更一般地，让 $A_n$ 是投资者在关闭账户后将收到的金额 $n$ 年 $(\mathrm{t}=\mathrm{n})$.

数学代写|金融数学代写Intro to Mathematics of Finance代考|SOME PRACTICAL ILLUSTRATIONS

作为一个简单的例子，考虑一个投资者，他与一家金融机构签订了一份合同，该金融机构提供 $£ 22,500$ 在 10 年结束时以单次付款换取 10,000 现在。如果投资者愿意将这笔资金占用 10 年，他是否签订合同的决定将取决于可用的另类投资。例如，如果投资者可以在其他地方获得末来 10 年的保证复利利率 $10 \%$ 每年，那么他不应该签订合同，因为，从方程式。 $1.3 .3 ， 10,000$ 英镑 $\times(1+10 \%)^{10}=£ 25,937.42$ ，大于 $£ 22,500$.
但是，如果他只能在末来 6 年内确定地获得这个利率，那么在决定是否签订合同时，他将不得不对他可能获得的利率做出判断。从现在起 6 年开始的 4 年期间。（请注意，在这些揷图中，我们忽略了进一步可能出现的复杂情况，例如税收的影响或提供合同的公司的可靠性。)
类似的考虑也适用于提出在给定期间结束时提供指定一次性付款以换取在整个期间定期支付一系列规定（通常是恒定 $)$ 金额的保费的合同。投资者是否会有利地考虑一份提供 $£ 3,500$ 在 10 年结束时免税，以换取 10 年的保费，每 $£ 200$ ，每年年初支付? 这个问题可以通过考虑每个单独的保费增长到 as 结束来回答，从方程。1.3.3，10,000 英镑 $\times(1+10 \%)^{10}=£ 25,937.42$ ，大于£22, 500 .
但是，如果他只能在末来 6 年内确定地获得这个利率，那么在决定是否签订合同时，他将不得不对他可能获得的利率做出判断。从现在起 6 年开始的 4 年期间。（请注意，在这些揷图中，我们忽略了进一步可能出现的复杂情况，例如税收的影响或提供合同的公司的可靠性。)
类似的考虑也适用于提出在给定期间结束时提供指定一次性付款以换取在整个期间定期支付一系列规定（通常是恒定) 金额的保费的合同。投资者是否会有利地考虑一份提供 $£ 3,500$ 在 10 年结束时免税，以换取 10 年的保费，每 $£ 200$ ，每年年初支付? 这个问题可以通过考虑在他在别处可用的特定复利利率下到 10 年期结束时的每个单独保费的增长情况来回答，并将所得值与 $\, 500$. 然而，更优雅的方法与第 3 章中介绍的年金概念有关。

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金融工程代写

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。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

数学代写|金融数学代写Intro to Mathematics of Finance代考|Find2022

Posted on 2022年10月31日2022年10月31日 by statistics-lab

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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
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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|Find2022

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

Interest may be regarded as a reward paid by one person or organization (the borrower) for the use of an asset, referred to as capital, belonging to another person or organization (the lender). The precise conditions of any transaction will be mutually agreed. For example, after a stated period of time, the capital may be returned to the lender with the interest due. Alternatively, several interest payments may be made before the borrower finally returns the asset.

Capital and interest need not be measured in terms of the same commodity, but throughout this book, which relates primarily to problems of a financial nature, we shall assume that both are measured in the monetary units of a given currency. When expressed in monetary terms, capital is also referred to as principal.

If there is some risk of default (i.e., loss of capital or non-payment of interest), a lender would expect to be paid a higher rate of interest than would otherwise be the case; this additional interest is known as the risk premium. The additional interest in such a situation may be considered as a further reward for the lender’s acceptance of the increased risk. For example, a person who uses his money to finance the drilling for oil in a previously unexplored region would expect a relatively high return on his investment if the drilling is successful, but might have to accept the loss of his capital if no oil were to be found. A further factor that may influence the rate of interest on any transaction is an allowance for the possible depreciation or appreciation in the value of the currency in which the transaction is carried out. This factor is obviously very important in times of high inflation.

It is convenient to describe the operation of interest within the familiar context of a savings account, held in a bank, building society, or other similar organization. An investor who had opened such an account some time ago with an initial deposit of $£ 100$, and who had made no other payments to or from the account, would expect to withdraw more than $£ 100$ if he were now to close the account. Suppose, for example, that he receives $£ 106$ on dosing his account.

This sum may be regarded as consisting of $£ 100$ as the return of the initial deposit and $£ 6$ as interest. The interest is a payment by the bank to the investor for the use of his capital over the duration of the account.

The most elementary concept is that of simple interest. This naturally leads to the idea of compound interest, which is much more commonly found in practice in relation to all but short-term investments. Both concepts are easily described within the framework of a savings account, as described in the following sections.

数学代写|金融数学代写Intro to Mathematics of Finance代考|SIMPLE INTEREST

Suppose that an investor opens a savings account, which pays simple interest at the rate of $9 \%$ per annum, with a single deposit of $£ 100$. The account will be credited with $£ 9$ of interest for each complete year the money remains on deposit. If the account is closed after 1 year, the investor will receive $£ 109$; if the account is closed after 2 years, he will receive $£ 118$, and so on. This may be summarized more generally as follows.

If an amount $C$ is deposited in an account that pays simple interest at the rate of $i$ per annum and the account is closed after $n$ years (there being no intervening payments to or from the account), then the amount paid to the investor when the account is closed will be
$$
C(1+n i)
$$
This payment consists of a return of the initial deposit $C$, together with interest
of amount
$$
n i C
$$
In our discussion so far, we have implicitly assumed that, in each of these last
two expressions, $n$ is an integer. However, the normal commercial practice in
relation to fractional periods of a year is to pay interest on a pro rata basis, so
that Eqs $1.2 .1$ and $1.2 .2$ may be considered as applying for all non-negative
values of $n$.
Note that if the annual rate of interest is $12 \%$, then $i=0.12$ per annum; if the annual rate of interest is $9 \%$, then $i=0.09$ per annum; and so on.

Note that in the solution to Example 1.2.1, we have assumed that 6 months and 10 months are periods of $1 / 2$ and 10/12 of 1 year, respectively. For accounts of duration less than 1 year, it is usual to allow for the actual number of days an account is held, so, for example, two 6-month periods are not necessarily regarded as being of equal length. In this case Eq. 1.2.1 becomes $$
C\left(1+\frac{m i}{365}\right)
$$
where $m$ is the duration of the account, measured in days, and $i$ is the annual rate of interest.

The essential feature of simple interest, as expressed algebraically by Eq. 1.2.1, is that interest, once credited to an account, does not itself earn further interest. This leads to inconsistencies that are avoided by the application of compound interest theory, as discussed in Section 1.3.

As a result of these inconsistencies, simple interest has limited practical use, and this book will, necessarily, focus on compound interest. However, an important commercial application of simple interest is simple discount, which is commonly used for short-term loan transactions, i.e., up to 1 year.

金融数学代考

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

利息可以被视为一个人或组织（借款人）为使用属于另一个人或组织（贷款人）的资产（称为资本）而支付的报酬。任何交易的确切条件将由双方商定。例如，在规定的时间段后，本金可能会连同到期利息退还给贷方。或者，在借款人最终归还资产之前，可能会支付数次利息。

资本和利息不必用同一种商品来衡量，但在本书中，主要涉及金融性质的问题，我们将假设两者都以给定货币的货币单位来衡量。当以货币形式表示时，资本也被称为本金。

如果存在一些违约风险（即资本损失或不支付利息），贷方将期望获得比其他情况更高的利率；这种额外的利息称为风险溢价。在这种情况下的额外利息可被视为对贷方接受增加的风险的进一步奖励。例如，一个人用自己的钱为以前未开发地区的石油钻探提供资金，如果钻探成功，他会期望他的投资回报相对较高，但如果没有石油，他可能不得不接受他的资本损失。被发现。可能影响任何交易的利率的另一个因素是进行交易的货币价值可能贬值或升值的准备金。

在银行、建筑协会或其他类似组织中持有的储蓄账户的熟悉环境中描述利息操作是很方便的。一位投资者在一段时间前开设了此类账户，初始存款为££100，并且没有向该账户支付其他款项或从该账户支付其他款项的人，预计提取的金额将超过££100如果他现在要关闭帐户。例如，假设他收到££106在给他的帐户加药。

这笔款项可被视为由££100作为初始押金的返还和££6作为利息。利息是银行向投资者支付的在账户存续期内使用其资金的款项。

最基本的概念是简单的兴趣。这自然会导致复利的想法，在实践中，除了短期投资之外，这种想法更为常见。如以下部分所述，这两个概念都可以在储蓄账户的框架内轻松描述。

数学代写|金融数学代写Intro to Mathematics of Finance代考|SIMPLE INTEREST

假设投资者开立一个储蓄账户，该账户支付单利，利率为 $9 \%$ 每年，单笔存款 $£ 100$. 该帐户将记入 $£ 9$ 每一整年的利息，这笔钱都留在存款中。如果账户在 1 年后关闭，投资者将收到 109 ; 如果帐户在 2 年后关闭，他将收到 118 等等。这可以更一般地概括如下。
如果金额 $C$ 存入支付单利的账户，利率为 $i$ 每年，账户在之后关闭 $n$ 年 (没有与账户之间的干预付款)，那么当账户关闭时支付给投资者的金额将是
$$
C(1+n i)
$$
此付款包括退还初始押金 $C$ ，连同金额的利息
$n i C$
到目前为止，在我们的讨论中，我们已经隐含地假设，在最后
两个表达式中的每一个中， $n$ 是一个整数。然而，与
一年的小数期相关的正常商业惯例是按比例支付利息，因此
Eqs1.2.1和1.2.2可以被认为适用于所有非
负值 $n$.
请注意，如果年利率为 $12 \%$ ，然后 $i=0.12$ 每年; 如果年利率为 $9 \%$ ，然后 $i=0.09$ 每年; 等等。
请注意，在示例 $1.2$. 1 的解决方案中，我们假设 6 个月和 10 个月是 $1 / 2$ 和 1 年的 10/12，分别。对于存续期少于 1 年的账户，通常会考虑账户持有的实际天数，因此，例如，两个 6 个月的期间不一定被视为长度相等。在这种情况下，方程式。1.2.1变成
$$
C\left(1+\frac{m i}{365}\right)
$$
在哪里 $m$ 是帐户的持续时间，以天为单位，并且 $i$ 是年利率。
单利的基本特征，由方程式代数表示。1.2.1，是利息，一旦记入账户，本身不会赚取更多的利息。如第 $1.3$ 节所述，这会导致应用复利理论避免的不一致。
由于这些不一致，单利在实际应用中受到了限制，本书必然会关注复利。然而，单利的一个重要商业应用是简单贴现，通常用于短期贷款交易，即最长为 1 年。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写