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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

## 数学代写|金融数学代写Intro to Mathematics of Finance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.

## 数学代写|金融数学代写Intro to Mathematics of Finance代考|Discounted Expected Value and the Time Value of Money

The previous simple example deals with randomness; however, it ignores two potentially important factors: time and risk. If the payoff to a security takes place one or more days into the future, or if the payoff contains a non-trivial degree of risk, then the equilibrium price of an asset will tend to be less than the expected payoff of the asset. The factors of time and risk can be very important. The issue of risk is an especially important issue that will be discussed extensively throughout this book. In this section, we turn out attention to the effect of time value while ignoring the risk discounting, noting that proper asset valuation requires the consideration of both the timing and risks of the asset’s cash flows, which we will discuss in Section 1.2.4.

The time value of money is the relationship between money at different points in time in the absence of risk. In finance, ignoring risk aversion, the time value of money is measured using the market prices of very low risk sovereign debt such as U.S. Treasury securities. Even though no assets are absolutely riskless, finance professionals describe short-term U.S. Treasuries as being riskless and describe their promised returns as “riskless” and their yields as risk-free rates.

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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。

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