## 金融代写|资产定价代写Asset Pricing代考|FIN50040

statistics-lab™ 为您的留学生涯保驾护航 在代写资产定价 Asset Pricing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。我们的专家在代写资产定价 Asset Pricing代写方面经验极为丰富，各种代写资产定价 Asset Pricing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|波动率模型代写Market Volatility Modelling代考|Critiques of Expected Utility Theory

This famous paradox, due to Allais (1953), challenges the von Neumann-Morgenstern framework. Consider a set of lotteries, each of which involves drawing one ball from an urn containing 100 balls, labeled $0-99$. Table $1.1$ shows the monetary prizes that will be awarded for drawing each ball, in four different lotteries $L^a, L^b, M^a$, and $M^b$.

Lottery $L^a$ offers $\$ 50$with certainty, while lottery$L^b$offers an$89 \%$chance of$\$50$, a $10 \%$ chance of $\$ 250$, and a$1 \%$chance of receiving nothing. Many people, confronted with this choice, prefer$L^a$to$L^b$even though the expected winnings are higher for lottery$L^b$. Lottery$M^a$offers an$11 \%$chance of winning$\$50$ and an $89 \%$ chance of receiving nothing, while lottery $M^b$ offers a $10 \%$ chance of winning $\$ 250$and a$90 \%$chance of receiving nothing. Many people, confronted with this choice, prefer$M^b$to$M^a$. The challenge to utility theory is that choosing$L^a$over$L^b$, while also choosing$M^b$over$M^a$, violates the independence axiom. As the structure of the table makes clear, the only difference between$L^a$and$L^b$is in the balls labeled 0-10; the balls labeled 11-99 are identical in these two lotteries. This is also true for the pair$M^a$and$M^b$. According to the independence axiom, the rewards for drawing balls 11-99 should then be irrelevant to the choices between$L^a$and$L^b$, and$M^b$and$M^a$. But if this is the case, then the two choices are the same because if one considers only balls$0-10, L^a$has the same rewards as$M^a$, and$L^b$has the same rewards as$M^b$. There is a longstanding debate over the significance of this paradox. Either people are easily misled (but can be educated) or the independence axiom needs to be abandoned. Relaxing this axiom must be done carefully to avoid creating further paradoxes (Chew 1983, Dekel 1986, Gul 1991).${ }^2$Recent models of dynamic decision making, notably the Epstein and Zin$(1989,1991)$preferences discussed in section 6.4, also relax the independence axiom in an intertemporal context, taking care to do so in a way that preserves time consistent decision making. 1.4.2 Rabin Critique Matthew Rabin (2000) has criticized utility theory on the ground that it cannot explain observed aversion to small gambles without implying ridiculous aversion to large gambles. This follows from the fact that differentiable utility has second-order risk aversion. ## 金融代写|波动率模型代写Market Volatility Modelling代考|Comparing Risks Earlier in this chapter we discussed the comparison of utility functions, concentrating on cases where two utility functions can be ranked in their risk aversion, with one turning down all lotteries that the other one turns down, regardless of the distribution of the risks. Now we perform a symmetric analysis, comparing the riskiness of two different distributions without making any assumptions on utility functions other than concavity. In this subsection we consider two distributions that have the same mean. Informally, there are three natural ways to define the notion that one of these distributions is riskier than the other: (1) All increasing and concave utility functions dislike the riskier distribution relative to the safer distribution. (2) The riskier distribution has more weight in the tails than the safer distribution. (3) The riskier distribution can be obtained from the safer distribution by adding noise to it. The classic analysis of Rothschild and Stiglitz (1970) shows that these are all equivalent. Consider random variables$\widetilde{X}$and$\widetilde{Y}$, which have the same expectation. (1)$\widetilde{X}$is weakly less risky than$\widetilde{Y}$if no individual with an increasing concave utility function prefers$\tilde{Y}$to$\tilde{X}$: $$E[u(\widetilde{X})] \geq E[u(\widetilde{Y})]$$ for all increasing concave$u$(.).$\widetilde{X}$is less risky than$\widetilde{Y}$(without qualification) if it is weakly less risky than$\widetilde{Y}$and there is some increasing concave$u($.$) which strictly$prefers$\widetilde{X}$to$\widetilde{Y}$. Note that this is a partial ordering. It is not the case that for any$\widetilde{X}$and$\widetilde{Y}$, either$\widetilde{X}$is weakly less risky than$\widetilde{Y}$or$\widetilde{Y}$is weakly less risky than$\widetilde{X}$. We can get a complete ordering if we restrict attention to a smaller class of utility functions than the concave, such as the quadratic. # 波动率模型代考 ## 金融代写|波动率模型代写Market Volatility Modelling代考|Critiques of Expected Utility Theory 这个由 Allais (1953) 提出的著名悖论挑战了 von Neumann-Morgenstern 框架。考虑一组彩票，每张彩票都涉及从装有 100 个球的罐子中抽出一个球，标记为0−99. 桌子1.1显示在四种不同的彩票中绘制每个球将获得的货币奖励大号一个,大号b,米一个， 和米b. 彩票大号一个提供$50有把握，而彩票大号b提供一个89%的机会$50， 一个10%的机会$250, 和一个1%什么都得不到的机会。很多人面对这个选择，更喜欢大号一个至大号b即使彩票的预期奖金更高大号b. 彩票米一个提供一个11%获胜的机会$50和89%抽奖时什么也得不到的机会米b提供一个10%获胜的机会$250和一个90%什么都得不到的机会。很多人面对这个选择，更喜欢米b至米一个.

1.4.2 Rabin 批判
Matthew Rabin (2000) 批评了效用理论，理由是它无法解释观察到的对小赌博的厌恶而不暗示对大赌博的荒谬厌恶。这是因为可微效用具有二阶风险规避这一事实。

## 金融代写|波动率模型代写Market Volatility Modelling代考|Comparing Risks

（1）所有递增和凹的效用函数都不喜欢相对于更安全的分布的风险更高的分布。
(2) 风险较高的分布比安全分布的尾部权重更大。
(3) 通过向安全分布中添加噪声，可以从更安全的分布中获得风险更高的分布。

(1)X~风险比是~如果没有一个具有递增的凹效用函数的人更喜欢是~至X~ :

## 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|资产定价代写Asset Pricing代考|FINS5576

statistics-lab™ 为您的留学生涯保驾护航 在代写资产定价 Asset Pricing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。我们的专家在代写资产定价 Asset Pricing代写方面经验极为丰富，各种代写资产定价 Asset Pricing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|波动率模型代写Market Volatility Modelling代考|The Arrow-Pratt Approximation

In the previous section, we defined the risk premium and certainty equivalent implicitly, as the solutions to equations (1.14) and (1.18). A famous analysis due to Arrow (1971) and Pratt (1964) shows that when risk is small, it is possible to derive approximate closedform solutions to these equations.

Consider a zero-mean risk $\tilde{y}=k \widetilde{x}$, where $k$ is a scale factor. Write the risk premium as a function of $k, g(k)=\pi\left(W_0, u, k \widetilde{x}\right)$. From the definition of the risk premium, we have
$$\mathrm{E} u\left(W_0+k \widetilde{x}\right)=u\left(W_0-g(k)\right) .$$
Note that $g(0)=0$, because you would pay nothing to avoid a risk with zero variability.
We now use the trick of repeated differentiation, in this case with respect to $k$, that was introduced in the previous subsection. Differentiating (1.20), we have
$$\mathrm{E}\left[\tilde{x} u^{\prime}\left(W_0+k \tilde{x}\right)\right]=-g^{\prime}(k) u^{\prime}\left(W_0-g(k)\right) \text {. }$$
At $k=0$, the left-hand side of (1.21) becomes $\mathrm{E}\left[\tilde{x} u^{\prime}\left(W_0\right)\right]=\mathrm{E}[\widetilde{x}] u^{\prime}\left(W_0\right)$, where we can bring $u^{\prime}\left(W_0\right)$ outside the expectations operator because it is deterministic. Since $\mathrm{E}[\tilde{x}]=0$, the left-hand side of (1.21) is zero when $k=0$, so the right-hand side must also be zero, which implies that $g^{\prime}(0)=0$.
We now differentiate with respect to $k$ a second time to get
$$\mathrm{E}^{-2} u^{\prime \prime}\left(w_o+k \bar{x}\right)=g^{\prime}(k)^2 u^{\prime \prime}\left(W_0-g(k)\right)-g^{\prime \prime}(k) u^{\prime}\left(W_0-g(k)\right) \text {, }$$
which implies that
$$g^{\prime \prime}(0)=\frac{-u^{\prime \prime}\left(W_0\right)}{u^{\prime}\left(W_0\right)} \mathrm{E} \widetilde{x}^2=A\left(W_0\right) \mathrm{E} \widetilde{x}^2$$

## 金融代写|波动率模型代写Market Volatility Modelling代考|Tractable Utility Functions

Almost all applied theory and empirical work in finance uses some member of the class of utility functions known as linear risk tolerance (LRT) or hyperbolic absolute risk aversion (HARA). Continuing to use wealth as the argument of the utility function, the HARA class of utility functions can be written as
$$u(W)=a+b\left(\eta+\frac{W}{\gamma}\right)^{1-\gamma}$$
defined for levels of wealth $W$ such that $\eta+W / \gamma>0$. The parameter $a$ and the magnitude of the parameter $b$ do not affect choices but can be set freely to deliver convenient representations of utility in special cases.

For these utility functions, risk tolerance-the reciprocal of absolute risk aversion-is given by
$$T(W)=\frac{1}{A(W)}=\eta+\frac{W}{\gamma},$$
which is linear in $W$. Absolute risk aversion itself is then hyperbolic in $W$ :
$$A(W)=\left(\eta+\frac{W}{\gamma}\right)^{-1}$$
Relative risk aversion is, of course,
$$R(W)=W\left(\eta+\frac{W}{\gamma}\right)^{-1}$$
There are several important special cases of HARA utility.
Quadratic utility has $\gamma=-1$. This implies that risk tolerance declines in wealth from (1.30), and absolute risk aversion increases in wealth from (1.31). In addition, the quadratic utility function has a “bliss point” at which $u^{\prime}=0$. These are important disadvantages, although quadratic utility is tractable in models with additive risk and has even been used in macroeconomic models with growth, where trending preference parameters are used to keep the bliss point well above levels of wealth or consumption observed in the data.

# 波动率模型代考

## 金融代写|波动率模型代写Market Volatility Modelling代考|The Arrow-Pratt Approximation

$$\mathrm{E} u\left(W_0+k \tilde{x}\right)=u\left(W_0-g(k)\right) .$$

$$\mathrm{E}\left[\tilde{x} u^{\prime}\left(W_0+k \tilde{x}\right)\right]=-g^{\prime}(k) u^{\prime}\left(W_0-g(k)\right) \text {. }$$

$$\mathrm{E}^{-2} u^{\prime \prime}\left(w_o+k \bar{x}\right)=g^{\prime}(k)^2 u^{\prime \prime}\left(W_0-g(k)\right)-g^{\prime \prime}(k) u^{\prime}\left(W_0-g(k)\right),$$

$$g^{\prime \prime}(0)=\frac{-u^{\prime \prime}\left(W_0\right)}{u^{\prime}\left(W_0\right)} \mathrm{E} \tilde{x}^2=A\left(W_0\right) \mathrm{E} \tilde{x}^2$$

## 金融代写|波动率模型代写Market Volatility Modelling代考|Tractable Utility Functions

(HARA) 的效用函数类别中的某些成员。继续使用财富作为效用函数的参数，HARA类效用函数可以写成
$$u(W)=a+b\left(\eta+\frac{W}{\gamma}\right)^{1-\gamma}$$

$$T(W)=\frac{1}{A(W)}=\eta+\frac{W}{\gamma}$$

$$A(W)=\left(\eta+\frac{W}{\gamma}\right)^{-1}$$

$$R(W)=W\left(\eta+\frac{W}{\gamma}\right)^{-1}$$
HARA 实用程序有几个重要的特例。

## 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|资产定价代写Asset Pricing代考|FN2190

statistics-lab™ 为您的留学生涯保驾护航 在代写资产定价 Asset Pricing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。我们的专家在代写资产定价 Asset Pricing代写方面经验极为丰富，各种代写资产定价 Asset Pricing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|波动率模型代写Market Volatility Modelling代考|Expected Utility

Standard microeconomics represents preferences using ordinal utility functions. An ordinal utility function $\Upsilon($.$) tells you that an agent is indifferent between x$ and $y$ if $\Upsilon(x)=\Upsilon(y)$ and prefers $x$ to $y$ if $\Upsilon(x)>\Upsilon(y)$. Any strictly increasing function of $\Upsilon($. will have the same properties, so the preferences expressed by $\Upsilon($.$) are the same as those$ expressed by $\Theta(\Upsilon()$.$) for any strictly increasing \Theta$. In other words, ordinal utility is invariant to monotonically increasing transformations. It defines indifference curves, but there is no way to label the curves so that they have meaningful values.

A cardinal utility function $\Psi($.$) is invariant to positive affine (increasing linear) trans-$ formations but not to nonlinear transformations. The preferences expressed by $\Psi($.$) are$ the same as those expressed by $a+b \Psi($.$) for any b>0$. In other words, cardinal utility has no natural units, but given a choice of units, the rate at which cardinal utility increases is meaningful.

Asset pricing theory relies heavily on von Neumann-Morgenstern utility theory, which says that choice over lotteries, satisfying certain axioms, implies maximization of the expectation of a cardinal utility function, defined over outcomes.

The content of von Neumann-Morgenstern utility theory is easiest to understand in a discrete-state example. Define states $s=1 \ldots S$, each of which is associated with an outcome $x_s$ in a set $X$. Probabilities $p_s$ of the different outcomes then define lotteries. When $S=3$, we can draw probabilities in two dimensions (since $p_3=1-p_1-p_2$ ). We get the so-called Machina triangle (Machina 1982), illustrated in Figure 1.1.

We define a compound lottery as one that determines which primitive lottery we are given. For example, a compound lottery $L$ might give us lottery $L^a$ with probability $\alpha$ and lottery $L^b$ with probability $(1-\alpha)$. Then $L$ has the same probabilities over the outcomes as $\alpha L^a+(1-\alpha) L^b$.

We define a preference ordering $\succeq$ over lotteries. A person is indifferent between lotteries $L^a$ and $L^b, L^a \sim L^b$, if and only if $L^a \succeq L^b$ and $L^b \succeq L^a$.
Next we apply two axioms of choice over lotteries.
Continuity axiom: For all $L^a, L^b, L^c$ s.t. $L^a \succeq L^b \succeq L^c$, there exists a scalar $\alpha \in[0,1]$ s.t.
$$L^b \sim \alpha L^a+(1-\alpha) L^c .$$
This axiom says that if three lotteries are (weakly) ranked in order of preference, it is always possible to find a compound lottery that mixes the highest-ranked and lowest-ranked lotteries in such a way that the economic agent is indifferent between this compound lottery and the middle-ranked lottery. The axiom implies the existence of a preference functional defined over lotteries, that is, an ordinal utility function for lotteries that enables us to draw indifference curves on the Machina triangle.

## 金融代写|波动率模型代写Market Volatility Modelling代考|Risk Aversion

We now assume the existence of a cardinal utility function and ask what it means to say that the agent whose preferences are represented by that utility function is risk averse. We also discuss the quantitative measurement of risk aversion.

To bring out the main ideas as simply as possible, we assume that the argument of the utility function is wealth. This is equivalent to working with a single consumption good in a static two-period model where all wealth is liquidated and consumed in the second period, after uncertainty is resolved. Later in the book we discuss richer models in which consumption takes place in many periods, and also some models with multiple consumption goods.

For simplicity we also work with weak inequalities and weak preference orderings throughout. The extension to strict inequalities and strong preference orderings is straightforward.

An important mathematical result, Jensen’s Inequality, can be used to link the concept of risk aversion to the concavity of the utility function. We start by defining concavity for a function $f$.

Definition. $f$ is concave if and only if, for all $\lambda \in[0,1]$ and values $a, b$,
$$\lambda f(a)+(1-\lambda) f(b) \leq f(\lambda a+(1-\lambda) b) .$$
If $f$ is twice differentiable, then concavity implies that $f^{\prime \prime} \leq 0$. Figure $1.2$ illustrates a concave function.

Note that because the inequality is weak in the above definition, a linear function is concave. Strict concavity uses a strong inequality and excludes linear functions, but we proceed with the weak concept of concavity.
Now consider a random variable $\tilde{z}$. Jensen’s Inequality states that
$$\mathrm{E} f(\bar{z}) \leq f(\mathrm{E} \bar{z})$$
for all possible $\tilde{z}$ if and only if $f$ is concave.

# 波动率模型代考

## 金融代写|波动率模型代写Market Volatility Modelling代考|Expected Utility

)tellsyouthatanagentisindifferentbetween $x$ 和 $y$ 如果 $\Upsilon(x)=\Upsilon(y)$ 并且喜欢 $x$ 至 $y$ 如果
$\Upsilon(x)>\Upsilon(y)$. 的任何严格增函数 $\Upsilon($. 将具有相同的属性，因此表示的偏好 $\Upsilon$ (.) arethesameasthose 表示为 $\Theta(\Upsilon()$.) foranystrictlyincreasing $\Theta$. 换句话说，序数效用对于单调递增的变换是不变的。它 定义了无差异曲线，但无法标记曲线以使它们具有有意义的值。

von Neumann-Morgenstern 效用理论的内容在一个离散状态的例子中最容易理解。定义状态 $s=1 \ldots S$ ，每一个都与一个结果相关联 $x_s$ 在一组 $X$. 概率 $p_s$ 不同的结果然后定义彩票。什么时候 $S=3$ ，我们可以绘制二维概率 (因为 $p_3=1-p_1-p_2$ ). 我们得到所谓的 Machina 三角形 (Machina 1982)，如图 $1.1$ 所示。

$$L^b \sim \alpha L^a+(1-\alpha) L^c .$$

## 金融代写|波动率模型代写Market Volatility Modelling代考|Risk Aversion

$$\lambda f(a)+(1-\lambda) f(b) \leq f(\lambda a+(1-\lambda) b) .$$

$$\operatorname{E} f(\bar{z}) \leq f(\mathrm{E} \bar{z})$$

## 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。