## 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

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

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

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

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

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

## 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|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 $£ 22,500$.

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 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.

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

$$[C(1+i)] \times(1+i)=C(1+i)^2=C\left(1+2 i+i^2\right)$$

## 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|Find2022

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 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.

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

$$C(1+n i)$$

$n i C$

Eqs1.2.1和1.2.2可以被认为适用于所有非

$$C\left(1+\frac{m i}{365}\right)$$

## 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|金融数学代写Financial Mathematics代考|MATH3090

statistics-lab™ 为您的留学生涯保驾护航 在代写金融数学Financial Mathematics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Financial Mathematics代写方面经验极为丰富，各种代写金融数学Financial Mathematics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|金融数学代写Financial Mathematics代考|The Limits to Arbitrage and Complete Markets

The models and intuition of earlier sections often relied on or described prices in frictionless markets wherein numerous investors such as speculators and arbitragers compete to earn higher returns. Financial economists often describe this condition of informational market efficiency as being when all available information becomes reflected in market prices such that it is not possible to utilize that information to consistently earn a riskadjusted abnormal profit (i.e., market participants cannot consistently identify mispriced securities).
A well-recognized problem with the theory of informationally efficient markets is that if available information is instantaneously incorporated into market prices then there will be no incentive for market participants to gather information and integrate that information into their investment decisions. If no one searches for mispriced securities then prices will not be efficient. In a perfectly efficient market everyone would adopt passive investment strategies which are buy-and-hold strategies with no attempt to trade in an effort to gain from mispriced securities.
Clearly no market can be perfectly efficient. The only meaningful issue is the extent to which markets approach informational efficiency.

The concept of inefficiently efficient markets is that securities are mispriced just enough and just often enough to attract a moderate number of active investment managers (managers that execute trades for the purpose of trying to improve risk-adjusted return) and active individual investors. The benefits and costs of active investing reach an equilibrium that results in a level of market inefficiency that sustains this equilibrium level of information analysis.

The primary purpose of derivatives is to facilitate risk management. Financial derivatives help to complete a market. Perfect completion of a market means that there are enough distinct investment opportunities available that investors can establish long and short positions in existing securities in a way that allows them to position their portfolio exactly as they desire. As an example, if a grocery store mixes apples, bananas, and cherries into three different types of fruit baskets, a customer may be inconvenienced by being unable to purchase one basket with exactly the amount of each type of fruit that she desires unless by chance one of the baskets exactly meets her preferences. However, if a customer is allowed to trade with the store and can buy and sell the different types of fruit baskets without trading costs, she will be able to obtain exactly the numbers of each type of fruit that she desires so long as the number of distinct fruit baskets being traded equals the number of different types of fruit (i.e., the market is complete). In a similar way, derivatives are created to move the market closer to completion so that market participants are better able to establish positions that move the participants closer to their desired risk exposures.
Financial derivatives can also be used to provide arbitragers, speculators, and investors with powerful tools with which to attempt to enhance their risk-adjusted returns through superior processing of available information. When those market participants with the greatest abilities to identify mispriced securities are enabled with superior tools such as derivatives to best utilize their abilities to buy underpriced assets and sell overpriced assets, the market prices of assets will tend to be better driven toward their intrinsic values. Because market prices provide the signals that guide production and consumption decisions throughout an economy, these arbitragers, speculators, and investors are unwittingly driving the decision making throughout the entire economy into being more and more efficient. Therefore, derivatives can play a role in increasing the efficiency in production and consumption decisions which in turn means improved economic growth and economic utility.

## 金融代写|金融数学代写Financial Mathematics代考|Chapter Demonstrating Exercises

A U.S.-based export firm will receive 10 million British pounds in three months. The firm can tolerate an exchange rate between $\$ 1.25$to$\$1.34$ U.S. dollars per pound to convert the pounds to its domestic currency (U.S. dollars), but is unwilling to bear the risk of converting the foreign exchange to U.S. dollars at an exchange rate of $\$ 1.25$or lower. On the other hand, the firm will be very content with an exchange rate of$\$1.34$ per British pound. How can a financial derivative strategy be designed to meet the needs of this U.S. export firm?

## 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。