Posted on Categories:Option Pricing Theory, 量化决策模型, 金融代写

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金融代写|量化决策模型代写Quantitative Decision Models 代考|Decision Making with Probabilities

In this approach, the decision-maker has information concerning the relative likelihood of each of the states of nature. It is sometimes called “decision making under uncertainty.” The criterion used in decision-making strategy with probabilities is to select that decision so as to maximize the expected value of the outcome. To illustrate the approach, let’s refer again to the payoff table for our make-buy example, this time adding a row for probabilities and a column for the expected value of the decision alternatives.

In decision analysis, it is assumed that the probabilities are long-term relative frequencies. Since they are often simply the subjective judgment of the decision- maker, the techniques is subject to the criticism of this limitation. But this criticism can be levied against any quantitative approach – the output is only as good as the input. To counter the criticism, we will add a sensitivity analysis step after the initial solution. For now, let’s learn the expected value approach.
The expected value (EV) for a decision alternative is the sum of the [probabilities of the states of nature times the payoffs]. For the “make product” decision:
\begin{aligned} \operatorname{EV}\left(d_1\right) &=\left[P\left(s_1\right)^* V_{11}\right]+\left[P\left(s_2\right)^* V_{12}\right] \ =& {[0.35 *-20,000]+[0.65 * 90,000] } \ &=\ 51,500 \end{aligned}
The EV of $\$ 51,500$represents the long run outcome of repeated “make product” experiments. That is, if we could theoretically conduct the “make product” decision 100 times, 35 times we would lose$\$20,000$, and 65 times we would make $\$ 90,000$. The weighted average of these outcomes is$\$51,500$. In reality, we do not conduct the experiment 100 times – we make the decision once and we are either going to lose $\$ 20,000$or make$\$90,000$. However, and this is very important, we use the expected value approach to assist us in making the decision.

I should add, at this point, that to abide by the laws of probability, each probability must be a real number between 0 and 1 , and the sum of the probabilities for the states of nature must sum to one. For this to happen, the states of nature must be mutually exclusive and exhaustive – that is, there cannot also be a state of nature called, for example, medium demand. If there was such a state of nature, it would have to be added to the payoff table and accounted for with a third probability.

金融代写|量化决策模型代写Quantitative Decision Models 代考|Using The Management Scientist for Decision Making with Probabilities

Let’s return to the software for a moment and rerun this example problem using the expected value criterion for selecting a decision alternative.
After you open “The Management Scientist” program, click on File, then New, then enter $\mathbf{3}$ decision alternatives, and $\mathbf{2}$ states of nature just as before. This time, select State of Nature Probabilities, and then click OK. Enter the numbers for the payoff table and the probabilities for the two states of nature. Next, select Solution, then Solve, and keep the default selection Maximize the Payoff. As before, you can print this solution, or better, save it to a file. I saved the solution to an Out file, then inserted it to this open Word document as before.

金融代写|量化决策模型代写Quantitative Decision Models 代考|Decision Making with Probabilities

$$\mathrm{EV}\left(d_1\right)=\left[P\left(s_1\right)^* V_{11}\right]+\left[P\left(s_2\right)^* V_{12}\right]=[0.35 *-20,000]+[0.65 * 90,000]=\ 51,500$$

金融代写|量化决策模型代写Quantitative Decision Models 代考|Using The Management Scientist for Decision Making with Probabilities

Solution，然后选择 Solve，并保持默认选择 Maximize the Payoff。和以前一样，您可以打印此解决方客，或者更好的是，将 其保存到文件中。我桨解决方宲保存到一个 Out 文件中，然后像以前一样将它揷入到这个打开的 Word 文档中。

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。