## 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?
Payoff in upstate $=\$ 16=$bond$+(h \times$call$)=\$7+(h \times \$ 3)$$$h=(\ 16-\ 7) / \ 3=3$$ ## 金融代写|金融数学代写Financial Mathematics代考|Popular Option Strategies with Multiple Positions Two of the most popular strategies involving options are covered calls and protective puts. Both of these strategies were illustrated in the examples in Section 1.5.1. A covered call is the simultaneous writing of a call option while having a long position in the underlying asset. A protective put is the simultaneous purchase of a put option while having a long position in the underlying asset. These two portfolios are depicted in Figure$1.8$and Figure$1.9$Note that the portfolio profits and losses in Figures$1.8$and$1.9$can be formed by summing the profits and losses of the portfolio’s component positions. In other words, at each point on the horizontal axis (i.e., each value of$S_T$), the profit or loss of the covered call or protective put is found by summing the profits and/or losses of the two positions that form them. Option spreads are simultaneous long and short positions in either different call options or different put options (but not both calls and puts). Three general types of option spread strategies are vertical spreads, horizontal spreads, and diagonal spreads. The terms describing the three spreads relate to the visualization of a matrix of option prices with strike price forming the vertical axis and expiration date forming the horizontal axis. Thus, in a vertical option spread, the options differ by strike price; in a horizontal option spread, the options differ by expiration date; and in a diagonal spread, they differ by both strike price and expiration date. This section focuses on the strategies with the same expiration date – vertical spreads. Figure$1.10$illustrates a vertical call spread known as a bull spread. The payout of a bull spread at expiration is positively related to the underlying asset, hence it is “bullish” with respect to the price of the underlying asset. The bullish nature of a bull spread occurs when the long call option position is in the option with the lower strike price and the short option position is in the asset with the higher strike price. Interestingly, the same bullish diagram can be generated using put options with the same structure: the long put option position is in the option with the lower strike price and the short option position is in the asset with the higher strike price. Figure$1.11$illustrates a vertical call spread known as a bear spread. Bear spreads reverse the direction of the options by establishing the long call option position in the option with the higher strike price and the short option position is in the asset with the lower strike price. Like in the case of bull spreads, the same bearish diagram can be generated using put options with the same structure: the long put option position is in the option with the higher strike price and the short option position is in the asset with the lower strike price. ## 金融数学代考 ## 金融代写|金融数学代写金融数学代考|无套利二项期权估值 无套利衍生品估值最吸引人的模型之一是二项期权定价模型。二项模型只允许一股股票在一段时间内的价值产生两种可能的结果。每种可能的结果都被称为“状态”，通常被描述为“向上状态”或“向下状态”。例如，考虑一股目前交易价格为每股$\$10$的股票，它被认为在一年底有两种可能的结果:如果情况顺利(上升状态)，它的价格为$\$ 16$;如果情况不顺利(下降状态)，它的价格为$\$7$。我们将股票的当前价格表示为$S_0$，将处于上涨状态的股价值表示为$S_u$，将处于下跌状态的股票值表示为$S_d$。图$1.6$说明了所有二项模型中最简单的一个时间段。现在考虑这只股票的看涨期权，在一个时期内到期，执行价为$\$ 13$。虽然我们还不知道该期权的市场价值$C_0$，但我们确实知道该期权在年底的价值($C_u$在上升状态，$C_d$在下降状态)从$\$3$在上升状态(发现为$\$ 16-\$13$)和$\$ 0$在下降状态(因为该期权没有被执行)的支付，如图1.7所示 注意，股票价格在两种状态(即$\$16-\$ 7$)之间的变化是$\$9$，而与此同时，期权价格只变化$\$ 3$。解决当前期权价格$\left(C_0\right)$的关键是要意识到期权的收益与股票的收益是完全相关的。唯一的区别是股价的变化是三倍，股价的最坏情况值是$\$7$，而期权的最坏情况值是$\$ 0$。这意味着一个套利者可以构建两个具有相同收益的投资组合，这被称为用一个投资组合复制另一个投资组合。这里，我们构建了两个投资组合:(1)一个或多个看涨期权加上一个无风险债券和(2)一股股票。这两种投资组合在期权到期时的收益是相同的。如果它们的收益相同，那么它们的现值也一定相同。用看涨期权和债券来复制股票，收益必须是相同的。第一步是要注意，如果期权到期时毫无价值，无风险债券的支付必须与下跌状态下的股票相同(在这种情况下是$\$7)$)。因此，无风险债券的面值必须为$\$ 7$。第二步是确定看涨期权的数量，这些看涨期权与债券相结合，在期权到期时提供的股息与北部州的股票(16美元)相同。看涨期权的数量$h$必须满足以下条件: 在上州的偿付$=\$16=$ bond $+(h \times$ call $)=\$ 7+(h \times \$3)$
$$h=(\ 16-\ 7) / \ 3=3$$

## 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|ACFl1003

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|Sequences of functions

Given a real interval $[a, b]$, we denote $\mathscr{F}([a, b])$ the collection of all real functions defined on $[a, b]$ :
$$\mathscr{F}([a, b])={f \mid f:[a, b] \rightarrow \mathbb{R}} .$$
Definition 2.2. A sequence of functions with domain $[a, b]$ is a sequence of elements of $\mathscr{F}([a, b])$.

Example 2.3. Functions $f_{n}(x)=x^{n}$, where $x \in[0,1]$, form a sequence of functions in $\mathscr{F}([0,1])$.

Let us analyse what happens when $n \rightarrow \infty$. It is easy to realise that a sequence of continuous functions may converge to a non-continuous function. Indeed, for the sequence of functions in Example 2.3, it holds:
$$\lim {n \rightarrow \infty} f{n}(x)=\lim {n \rightarrow \infty} x^{n}= \begin{cases}1 & \text { if } \quad x=1 \ 0 & \text { if } \quad 0 \leq x<1\end{cases}$$ Thus, even if every function of the sequence $f{n}(x)=x^{n}$ is continuous, the limit function $f(x)$, defined below, may not be continuous:
$$f(x):=\lim {n \rightarrow \infty} f{n}(x) .$$
The convergence of a sequence of functions, like that of Example 2.3, is called simple convergence. We now provide its rigorous definition.

## 金融代写|金融数学代写Financial Mathematics代考|Uniform convergence

Pointwise convergence does not allow, in general, interchanging between limit and integral operators, a possibility that we call passage to the limit and that we also address in $\S$ 8.10. To explain it, consider the sequence of functions:
$$f_{n}(x)=n e^{-n^{2} x^{2}}$$
defined on $[0, \infty)$; it is a sequence that clearly converges to the zero function. Employing the substitution $n x=y$, evaluation of the integral of $f_{n}$ yields:
$$\int_{0}^{\infty} f_{n}(x) \mathrm{d} x=\int_{0}^{\infty} e^{-y^{2}} \mathrm{~d} y$$
We do not have the tools, yet, to evaluate the integral in the left-hand side of the above equality (but we will soon), but it is clear that it is a positive real number, so we have:
$$\lim {n \rightarrow \infty} \int{0}^{\infty} f_{n}(x) \mathrm{d} x=\int_{0}^{\infty} e^{-y^{2}} \mathrm{~d} y=\alpha>0 \neq \int_{0}^{\infty} \lim {n \rightarrow \infty} f{n}(x) \mathrm{d} x=0 .$$
To establish a ‘good’ notion of convergence, that allows the passage to the limit, when we take the integral of the considered sequence, and that preserves continuity, we introduce the fundamental notion of uniform convergence.

## 金融代写|金融数学代写Financial Mathematics代考|Sequences of functions

$$\mathscr{F}([a, b])=f \mid f:[a, b] \rightarrow \mathbb{R} .$$

$$\lim n \rightarrow \infty f n(x)=\lim n \rightarrow \infty x^{n}={1 \quad \text { if } \quad x=10 \quad \text { if } \quad 0 \leq x<1$$

$$f(x):=\lim n \rightarrow \infty f n(x) .$$

## 金融代写|金融数学代写Financial Mathematics代考|Uniform convergence

$$f_{n}(x)=n e^{-n^{2} x^{2}}$$

$$\int_{0}^{\infty} f_{n}(x) \mathrm{d} x=\int_{0}^{\infty} e^{-y^{2}} \mathrm{~d} y$$

$$\lim n \rightarrow \infty \int 0^{\infty} f_{n}(x) \mathrm{d} x=\int_{0}^{\infty} e^{-y^{2}} \mathrm{~d} y=\alpha>0 \neq \int_{0}^{\infty} \lim n \rightarrow \infty f n(x) \mathrm{d} x=0$$

## 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。

## 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|Limits of functions

A vector function is a function $f$ of the form $f: A \rightarrow \mathbb{R}^{m}$, where $A \subset \mathbb{R}^{n}$. Since $f(\boldsymbol{x}) \in \mathbb{R}^{m}$ for each $\boldsymbol{x} \in A$, then there are $m$ functions $f_{j}: A \rightarrow \mathbb{R}$, calléd component functions ớ $f$, such that:
$$f(\boldsymbol{x})=\left(f_{1}(\boldsymbol{x}), \ldots, f_{m}(\boldsymbol{x})\right) \quad \text { for each } \quad \boldsymbol{x} \in A$$
When $m=1$, function $f$ has only one component and we call $f$ real-valued. If $f=\left(f_{1}, \ldots, f_{m}\right)$ is a vector function, where the components $f_{j}$ have intrinsic domains, then the maximal domain of $f$ is defined to be the intersection of the domains of all components $f_{j}$.

To set up a notation for the algebra of vector functions, let $E \subset \mathbb{R}^{n}$ and let $f, g: E \rightarrow \mathbb{R}^{m}$. For each $x \in E$, the following operations can be defined.
The scalar multiple of $\alpha \in \mathbb{R}$ by $f$ is given by:
$$(\alpha f)(\boldsymbol{x}):=\alpha f(\boldsymbol{x}) .$$
The sum of $f$ and $g$ is obtained as:
$$(f+g)(\boldsymbol{x}):=f(\boldsymbol{x})+g(\boldsymbol{x}) .$$
The (Euclidean) dot product of $f$ and $g$ is constructed as:
$$(f \cdot g)(\boldsymbol{x}):=f(\boldsymbol{x}) \cdot g(\boldsymbol{x}) .$$

## 金融代写|金融数学代写Financial Mathematics代考|Sequences and series of real or complex numbers

A sequence is a set of numbers $u_{1}, u_{2}, u_{3}, \ldots$, in a definite order of arrangement, that is, a map $u: \mathbb{N} \rightarrow \mathbb{R}$ or $u: \mathbb{N} \rightarrow \mathbb{C}$, formed according to a certain rule. Each number in the sequence is called term; $u_{n}$ is called the $n^{\text {th }}$ term. The sequence is called finite or infinite, according to the number of terms. The sequence $u_{1}, u_{2}, u_{3}, \ldots$, when considered as a function, is also designated as $\left(u_{n}\right){n \in \mathbb{N}}$ or briefly $\left(u{n}\right)$.

Definition 2.1. The real or complex number $\ell$ is called the limit of the infinite sequence $\left(u_{n}\right)$ if, for any positive number $\varepsilon$, there exists a positive number $n_{\varepsilon}$, depending on $\varepsilon$, such that $\left|u_{n}-\ell\right|<\varepsilon$ for all integers $n>n_{\varepsilon}$. In such a case, we denote:
$$\lim {n \rightarrow \infty} u{n}=\ell$$
Given a sequence $\left(u_{n}\right)$, we say that its associated infinite series $\sum_{n=1}^{\infty} u_{n}$ :
(i) converges, when it exists the limit:
$$\lim {n \rightarrow \infty} \sum{k=1}^{n} u_{k}:=S=\sum_{n=1}^{\infty} u_{n}$$
(ii) diverges, when the limit of the partial sums $\sum_{k=1}^{n} u_{k}$ does not exist.

## 金融代写|金融数学代写Financial Mathematics代考|Limits of functions

$$f(\boldsymbol{x})=\left(f_{1}(\boldsymbol{x}), \ldots, f_{m}(\boldsymbol{x})\right) \quad \text { for each } \quad \boldsymbol{x} \in A$$

$$(\alpha f)(\boldsymbol{x}):=\alpha f(\boldsymbol{x})$$

$$(f+g)(\boldsymbol{x}):=f(\boldsymbol{x})+g(\boldsymbol{x}) .$$

$$(f \cdot g)(\boldsymbol{x}):=f(\boldsymbol{x}) \cdot g(\boldsymbol{x})$$

## 金融代写|金融数学代写Financial Mathematics代考|Sequences and series of real or complex numbers

$$\lim n \rightarrow \infty u n=\ell$$

(i) 收敛，当它存在极限时:
$$\lim n \rightarrow \infty \sum k=1^{n} u_{k}:=S=\sum_{n=1}^{\infty} u_{n}$$
(ii) 发散，当部分和的限制 $\sum_{k=1}^{n} u_{k}$ 不存在。

## 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|ACTL20001

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|Euclidean space

If $n \in \mathbb{N}$, we use the symbol $\mathbb{R}^{n}$ to indicate the Cartesian ${ }^{1}$ product of $n$ copies of $\mathbb{R}$ with itself, i.e.:
$$\mathbb{R}^{n}:=\left{\left(x_{1}, x_{2}, \ldots, x_{n}\right) \mid x_{j} \in \mathbb{R} \text { for } j=1,2, \ldots, n\right} .$$
The concept of Euclidean ${ }^{2}$ space is not limited to the set $\mathbb{R}^{n}$, but it also includes the so-called Euclidean inner product, introduced in Definition 1.1. The integer $n$ is called dimension of $\mathbb{R}^{n}$, the elements $x=\left(x_{1}, x_{2}, \ldots, x_{n}\right)$ of $\mathbb{R}^{n}$ are called points, or vectors or ordered $n$-tuples, while $x_{j}, j=1, \ldots, n$, are the coordinates, or components, of $\boldsymbol{x}$. Vectors $\boldsymbol{x}$ and $\boldsymbol{y}$ are equal if $x_{j}=y_{j}$ for $j=1,2, \ldots, n$. The zero vector is the vector whose components are null, that is, $\mathbf{0}:=(0,0, \ldots, 0)$. In low dimension situations, i.e. for $n=2$ or $n=3$, we will write $\boldsymbol{x}=(x, y)$ and $\boldsymbol{x}=(x, y, z)$, respectively.

For our purposes, that is extending differential calculus to functions of several variables, we need to define an algebraic structure in $\mathbb{R}^{n}$. This is done by introducing operations in $\mathbb{R}^{n}$.

Definition 1.1. Let $\boldsymbol{x}=\left(x_{1}, x_{2}, \ldots, x_{n}\right), \boldsymbol{y}=\left(y_{1}, y_{2}, \ldots, y_{n}\right) \in \mathbb{R}^{n}$ and $\alpha \in \mathbb{R}$
(i) The sum of $\boldsymbol{x}$ and $\boldsymbol{y}$ is the vector:
$$\boldsymbol{x}+\boldsymbol{y}:=\left(x_{1}+y_{1}, x_{2}+y_{2}, \ldots, x_{n}+y_{n}\right) ;$$

(ii) The difference of $\boldsymbol{x}$ and $\boldsymbol{y}$ is the vector:
$$\boldsymbol{x}-\boldsymbol{y}:=\left(x_{1}-y_{1}, x_{2}-y_{2}, \ldots, x_{n}-y_{n}\right)$$
(iii) The $\alpha$-multiple of $\boldsymbol{x}$ is the vector:
$$\alpha \boldsymbol{x}=\left(\alpha x_{1}, \alpha x_{2}, \ldots, \alpha x_{n}\right) ;$$
(iv) The Euclidean inner product of $\boldsymbol{x}$ and $\boldsymbol{y}$ is the real number:
$$\boldsymbol{x} \cdot \boldsymbol{y}:=x_{1} y_{1}+x_{2} y_{2}+\ldots+x_{n} y_{n} .$$

## 金融代写|金融数学代写Financial Mathematics代考|Topology of R

Topology, that is the description of the relations among subsets of $\mathbb{R}^{n}$, is based on the concept of open and closed sets, that generalises the notion of open and closed intervals. After introducing these concepts, we state their most basic properties. The first step is the natural generalisation of intervals in $\mathbb{R}^{n}$

Definition 1.13. Open and closed balls are defined as follows:
(i) $\forall r>0$, the open ball, centered at $a$, of radius $r$, is the set of points:
$$B_{r}(\boldsymbol{a}):=\left{\boldsymbol{x} \in \mathbb{R}^{n} \mid|\boldsymbol{x}-\boldsymbol{a}|<r\right} ;$$
(ii) $\forall r \geq 0$, the closed ball, centered at $\boldsymbol{a}$, of radius $r$, is the set of points:
$$\bar{B}_{r}(\boldsymbol{a})\left{\boldsymbol{x} \in \mathbb{R}^{n}|| \mid \boldsymbol{x}-\boldsymbol{a} | \leq r\right}$$
Note that, when $n=1$, the open ball centered at $a$ of radius $r$ is the open interval $(a-r, a+r)$, and the corresponding closed ball is the closed interval $[a-r, a+r]$. Here we adopt the convention of representing open balls as dashed circumferences, while closed balls are drawn as solid circumferences, as shown in Figure $1.4 .$

## 金融代写|金融数学代写Financial Mathematics代考|Euclidean space

$\backslash$ Imathbb ${R} \wedge{n}:=\backslash$ left $\left{\backslash\right.$ left $\left(x_{-}{1}, x_{-}{2}, \backslash\right.$ dots, $x_{-}{n} \backslash$ right) $\backslash$ mid $\left.\left.x_{-}\right} j\right}$ in $\backslash$ mathbb ${R} \backslash$ text ${$ for $} j=1,2, \backslash$ dots, $n \backslash$ right $}$ 。

$(-)$ 总和 $\boldsymbol{x}$ 和 $\boldsymbol{y}$ 是向量:
$$\boldsymbol{x}+\boldsymbol{y}:=\left(x_{1}+y_{1}, x_{2}+y_{2}, \ldots, x_{n}+y_{n}\right)$$
(ii) 差异 $\boldsymbol{x}$ 和 $\boldsymbol{y}$ 是向量:
$$\boldsymbol{x}-\boldsymbol{y}:=\left(x_{1}-y_{1}, x_{2}-y_{2}, \ldots, x_{n}-y_{n}\right)$$
(iii) $\alpha$ – 倍数 $\boldsymbol{x}$ 是向量:
$$\alpha \boldsymbol{x}=\left(\alpha x_{1}, \alpha x_{2}, \ldots, \alpha x_{n}\right)$$
(iv) 的欧几里得内积 $\boldsymbol{x}$ 和 $\boldsymbol{y}$ 是实数:
$$\boldsymbol{x} \cdot \boldsymbol{y}:=x_{1} y_{1}+x_{2} y_{2}+\ldots+x_{n} y_{n}$$

## 金融代写|金融数学代写Financial Mathematics代考|Topology of R

(i) $\forall r>0$ ，开球, 以 $a$, 半径 $r$ ，是点的集合:
(二) $\forall r \geq 0$, 封闭球, 以 $\boldsymbol{a}$, 半径 $r$, 是点的集合:

## 有限元方法代写

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

## MATLAB代写

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

## 金融代写|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|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 orange juice when the weather is forecasted, not just when the damage is 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 that future price changes will be 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.

## 金融代写|金融数学代写Financial Mathematics代考|Expected Value as a Foundation of Asset Valuation

The starting point for valuing a financial asset is that the price of the asset should reflect the expected cash inflows that the asset offers. We know that future cash flows are uncertain. In order to find expected cash flows, we have to use probability models to model the likelihood of cash flows occurring. Let’s review some mathematics with a focus on expected value.

Expected value’s intuitive meaning is that it is a long-run average. If a random variable is sampled many times, the long-run average of these sampled values is the expected value of the variable. We begin by reviewing how to calculate expected value from probability model perspective.

In a competitive market, a financial asset’s price is determined by supply and demand. To simplify an example, let’s consider an asset that will distribute its final cash flow to the owner of the asset immediately (e.g., before the end of the day). Financial analysts compete to identify and purchase assets with current market prices below the asset’s expected distribution (i.e., final payoff) and to identify and sell assets with current market prices above their expected payoff. Thus the expected value of the random payoff of a financial asset drives the current market price of the asset. Throughout this book, we assume that financial analysts have estimates of the probability distribution of these random variables (i.e., asset or security prices). Without going into detail here about how the values of expected cash flows are adjusted for time (i.e., for the delay between buying an asset and receiving its payoffs) and risk (i.e., the uncertainty of the size and timing of future payoffs), the value of a financial asset or contract is based on expected cash flows as indicated in Basic Principle 1.1.

Let’s look at some simple examples of assets or contracts with random future payoffs and calculate their expected values. To simplify the first example, future cash flows are not discounted for time or risk. Later examples in this chapter include discounting for time and risk.

## 有限元方法代写

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

## MATLAB代写

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

## 金融代写|金融数学代写Financial Mathematics代考|ACTL20001

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 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 1970 s. 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 dircct 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).

## 金融代写|金融数学代写Financial Mathematics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 to 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 gains $\$ X$if the stock declines$\$X$ over the life of the short sale and loses $\$ X$if the stock 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 hoth 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.

## 金融代写|金融数学代写Financial Mathematics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。

## 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|MATHS 1009

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|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.

## 金融代写|金融数学代写Financial Mathematics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.

## 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|ACTL20001

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|Annuities Payable at Different Frequencies than Interest Is Convertible

Method One: Convert the conversion period of the interest to the period of the payments.

The simplest way to deal with the case in which the annuity payments are made at a different frequency than the interest conversion frequency is to convert the interest to the equivalent rate convertible at the period of the annuity payments. After that is done, we do all of our calculations using the period of the annuity payments.

We begin with an annuity-immediate paying $\$ R$at the end of each five periods for a total of$n$interest conversion periods. To compute the present value, we sum the present value of each payment. Since it is delayed by$k$interest conversion periods, its present value is$v^{k}$. Each subsequent payment is delayed by an additional$kconversion periods. The present value of the annuity at inception is thus: \begin{aligned} P V &=R\left(v^{k}+v^{2 k}+\cdots v^{\frac{n}{k} k}\right) \ &=R v^{k}\left(1+v^{k}+\cdots+v^{n-k}\right) \ &=R v^{k} \frac{1-v^{n}}{1-v^{k}} \ &=R \frac{a_{\text {꾜 }, i}}{s_{\text {ㅈ, }, i}} \end{aligned} The accumulated value immediately after the last payment is made is computed by multiplying the expression in4.36$by$(1+i)^{n}$We can use this same technique to find the present and future (accumulated) values of annuities for which payments are made at the beginning of each$k$interest conversion periods. ## 金融代写|金融数学代写Financial Mathematics代考|Annuities Paid More Frequently than Interest Is Converted We already know how to do these problems by converting the interest rate to the period of the annuity payments. In this section we develop an alternative method which avoids the conversion problem. We assume that$m$payments are made during each interest conversion period and that there are a total of$n$interest conversion periods. There are thus$m n$payments in all. We assume that the amount of each payment is$\frac{R}{m}$(for a total of$\$R$ each period!).

The symbol $a_{\bar{n}}^{(m)}$ we will used to denote the present value of an annuityimmediate in this situation. Note the similarity to the symbol $i^{(m)}$ which represents the nominal annual rate of interest compounded $m$ times per year.

Remember: $n$ represents the period of the annuity in interest conversion periods and $m$ is the number of payments per interest conversion period.

We compute the present value by summing the appropriate geometric series:
\begin{aligned} a_{\bar{n}}^{(m)} &=\frac{1}{m}\left(v^{\frac{1}{m}}+v^{\frac{2}{m}}+\cdots+v^{n}\right) \ &=\frac{1}{m} \frac{v^{\frac{1}{m}}-v^{n+\frac{1}{m}}}{1-v^{\frac{1}{m}}} \ &=\frac{1}{m} \frac{v^{\frac{1}{m}}}{v^{\frac{1}{m}}}\left(\frac{1-v^{n}}{\left(\frac{1}{v^{\frac{1}{m}}}\right)-1}\right) \ &=\frac{1-v^{n}}{m\left((1+i)^{\frac{1}{m}}-1\right)} \ &=\frac{1-v^{n}}{i^{(m)}}=i \cdot\left(\frac{a_{\text {m, }, i}}{i^{(m)}}\right) \end{aligned}
Here we have used the symbol $i^{(m)}=m\left((1+i)^{\frac{1}{m}}-1\right)$ from an earlier chapter. The accumulated value of this annuity immediately after the last payment is made is denoted by $s_{\bar{n}}^{(m)}$ and is simply the value of $a_{\bar{n}}^{(m)}$ accumulated over the $n$ interest conversion periods.
\begin{aligned} s_{\bar{n}}^{(m)} &=a_{\bar{n}}^{(m)}(1+i)^{n} \ &=\frac{(1+i)^{n}-1}{i(m)} \ &=i \cdot\left(\frac{s_{\text {司, } i}}{i^{(m)}}\right) \end{aligned}

## 金融代写|金融数学代写Financial Mathematics代考|Annuities Payable at Different Frequencies than Interest Is Convertible

TI BA II Plus 解决方案：（表 4.44）我们使用 TVM 键计算利率和未来价值。

## 金融代写|金融数学代写Financial Mathematics代考|Alternative Method: Annuities Payable Less Frequently than Interest Is Convertible

꾜ㅈ磷在=R(在ķ+在2ķ+⋯在nķķ) =R在ķ(1+在ķ+⋯+在n−ķ) =R在ķ1−在n1−在ķ =R一个꾜 ,一世s兆， ,一世

## 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。