### 金融代写|金融数学代写Financial Mathematics代考|Overview and Mathematical Prerequisites

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• 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|Calculators and Computers

Because the calculations are often tedious if done on a standard calculator, you should purchase a financial calculator, especially if you intend to take the SOA/CAS common exam on Financial Mathematics (FM). Here is a list of the acceptable calculators as provided by the SOA website:

Calculators – For all exams (except EA exams): only the following Texas Instrument calculator models may be used:

• BA-35 TI-30Xa
• BA II Plus* TI-30XIIS*
• BA II Plus Professional Edition* TI-30XIIB*
• TI-30XS MultiView* TI-30XB MultiView*
• Upon entrance to the exam room, candidates must show the supervisor that the memory has been cleared. For the BA II Plus and the BA II Plus Professional Edition, clearing will reset the calculator to the factory default settings.

You may bring 2 calculators into the exam room. They should be these two:
TI BA II Plus Professional Edition TI-30XS MultiView
Keystroke instruction will be provided within this text for the TI BA II Plus and TI BA II Plus Professional as well as the TI-30XS MultiView. Prior to using your TI BA II Plus you should go to the Appendix: Basic Setup and change some of the default settings. Most of the examples in the text will be worked out using the TI BA II Plus, and the keystrokes will be presented as part of the solution.

Please be aware that not all of the problems on the FM exam can be solved using only the financial functions on the calculator. You will need to know the formulas and how to use them! Indeed, some of the questions asked require that you recognize various forms of the important formulas.

## 金融代写|金融数学代写Financial Mathematics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}

## 金融代写|金融数学代写Financial Mathematics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.”

## 金融代写|金融数学代写Financial Mathematics代考|Calculators and Computers

• BA-35 TI-30Xa
• BA II Plus* TI-30XIIS*
• BA II Plus 专业版* TI-30XIIB*
• TI-30XS 多视图* TI-30XB 多视图*
• 进入考场后，考生必须向考官出示记忆已被清除的情况。对于 BA II Plus 和 BA II Plus 专业版，清除会将计算器重置为出厂默认设置。

TI BA II Plus 专业版 TI-30XS MultiView

## 金融代写|金融数学代写Financial Mathematics代考|Sequences and Series

∑一世=0n−1一个在一世=一个+一个在+一个在2+⋯+一个在n−1=一个1−在n1−在

∑一世=0∞一个在一世=林n→∞一个1−在n1−在=一个1−在

## 金融代写|金融数学代写Financial Mathematics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。

## 有限元方法代写

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## MATLAB代写

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