金融代写|资产定价代写Asset Pricing代考|FIN50040

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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|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

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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。