### 金融代写|风险理论代写Risk theory代考|STAT553

statistics-lab™ 为您的留学生涯保驾护航 在代写风险理论Risk theory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。我们的专家在代写风险理论Risk theory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|风险理论代写Risk theory代考|Actuarial Versus Financial Pricing

The last decades have seen the areas of insurance mathematics and mathematical finance coming closer together. One reason is the growing linking of pay-outs of life insurances and pension plans to the current value of financial products, another that certain financial products have been designed especially to be of interest for the insurance industry (see below). Nevertheless, some fundamental differences remain, and the present section aims at explaining some of these, with particular emphasis on the principles for pricing insurance products, resp. financial products.

In insurance, expected values play a major role. For example, let a claim $X \geq 0$ be the amount of money the insurance company has to pay out for a fire insurance on a given house next year (of course, $\mathbb{P}(X=0)$ is close to 1 !). The insurance company then ideally charges $H(X)=\mathbb{E} X$ in premium plus some loading, that is, an extra amount to cover administration costs, profit, risk etc. (different rules for the form of this loading are discussed in Sect. 3). The philosophy behind this is that charging premiums smaller than expected values in the long run results in an overall loss. This is a consequence of the law of large numbers (LLN). In its simplest form it says that if the company faces $n$ i.i.d. claims $X_1, \ldots, X_n$ all distributed as $X$, then the aggregate claim amount $A=X_1+\cdots+X_n$ is approximately $n \mathbb{E} X$ for $n$ large. Therefore, if the premium $H$ is smaller than $\mathbb{E} X$, then with high probability the total premiums $n H$ are not sufficient to cover the total aggregate claims $A$.

This argument carries far beyond this setting of i.i.d. claims, which is of course oversimplified: even in fire insurance, individual houses are different (the area varies, a house may have different types of heating, thatched roof or tiles, etc), and the company typically has many other lines of business such as car insurance, accident insurance, life insurance, etc. Let the claims be $X_1, X_2, \ldots$ Then the asymptotics
$$\frac{X_1+\cdots+X_n}{\mathbb{E} X_1+\cdots+\mathbb{E} X_n} \rightarrow 1$$
holds under weak conditions. For example, the following elementary result is sufficiently general to cover a large number of insurance settings

The standard setting for discussing premium calculation in the actuarial literature is in terms of a single risk $X \geq 0$ and does not involve portfolios, stochastic processes, etc. Here $X$ is an r.v. representing the random payment (possibly 0 ) to be made from the insurance company to the insured. A premium rule is then a $\lfloor 0, \infty)$-valued function $H$ of the distribution of $X$, often written $H(X)$, such that $H(X)$ is the premium to be paid, i.e. the amount for which the company is willing to insure the given risk. From an axiomatic point of view, the concept of premium rules is closely related to that of risk measures, to which we return in Sect. X.1.

The standard premium rules discussed in the literature (not necessarily the same as those used in practice!) are the following:

• The net premium principle $H(X)=\mathbb{E} X$ (also called the equivalence principle). As follows from a suitable version of the CLT that this principle will lead to a substantial loss if many independent risks are insured. This motivates that a loading should be added, as in the next principles:
• The expected value principle $H(X)=(1+\eta) \mathbb{E} X$, where $\eta$ is a specified safety loading. For $\eta=0$, we are back to the net premium principle. A criticism of the expected value principle is that it does not take into account the variability of $X$. This leads to:
• The variance principle $H(X)=\mathbb{E} X+\eta \operatorname{Var}(X)$. A modification (motivated by $\mathbb{E} X$ and $\operatorname{Var}(X)$ not having the same dimension) is
• The standard deviation principle $H(X)=\mathbb{E} X+\eta \sqrt{\operatorname{Var}(X)}$.

## 金融代写|风险理论代写Risk theory代考|Actuarial Versus Financial Pricing

$$\frac{X_1+\cdots+X_n}{\mathbb{E} X_1+\cdots+\mathbb{E} X_n} \rightarrow 1$$

• 净保费原则 $H(X)=\mathbb{E} X$ (也称为等价原则) 。从一个合适的 $\mathrm{CLT}$ 版本可以看出，如果许多独立风险被投 保，这一原则将导致重大损失。这促使应该添加负载，如下面的原则:
• 期望值原则 $H(X)=(1+\eta) \mathbb{E} X$ ，在哪里 $\eta$ 是指定的安全载荷。为了 $\eta=0$ ，我们又回到了净溢价原则。 对期望值原则的一个批评是它没有考虑到 $X$. 这将导致:
• 方差原理 $H(X)=\mathbb{E} X+\eta \operatorname{Var}(X)$. 修改 (动机是 $\mathbb{E} X$ 和 $\operatorname{Var}(X)$ 尺寸不同) 是
• 标准差原则 $H(X)=\mathbb{E} X+\eta \sqrt{\operatorname{Var}(X)}$.

## 广义线性模型代考

statistics-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。