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# 金融代写|随机控制理论代写STOCHASTIC CONTROL代考|MA547 Introduction and objectives

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## 金融代写|随机控制理论代写STOCHASTIC CONTROL代考|Introduction and objectives

Stochastic optimization is used in many industries to take decisions facing some uncertainties in the future. The asset to optimize can be a network (railway, telecommunication [Charalambous et al. (2005)] ), some exotic financial options of american type [Hull (2008)]. In the energy industry, a gaz company may want to optimize the use of a gaz storage [Chen \& Forsyth (2009)], [Ludkovski \& Carmona (2010, to appear)]. An electricity company may want to optimize the value of a powerplant [Porchet et al. (2009)] facing a price signal and dealing with operational contraints: ramp contraints, minimum on-off times, maximum number of start up during a period.
An integrated energy company may want to maximize an expected revenue coming from many decisions take:

• which thermal assets to use ?
• how should be managed the hydraulic reservoirs?
• which customers options to exercice?
• how should the physical portfolio be hedged with future contracts?
In the previous example, due to the structure of the energy market with limited liquidity, the management of a future position on the market can be seen as the management of a stock of energy available at a given price. So the problem can be seen as an optimization problem

## 金融代写|随机控制理论代写STOCHASTIC CONTROL代考|Stochastic control optimization and simulation

We give a simplified view of a stochastic control optimization problem. Supposing that the problem we propose to solve can be set as:
$$\text { minimize } \mathbb{E}\left(\sum_{t=1}^N \phi\left(t, \xi_t, n c_t\right)\right)$$
where $\phi$ is a cost function depending on time, the state variable $\xi_t$ (stock and uncertainty,) and depending on the command $n c_t$ realized at date $t$. For simplicity, we suppose that the control only acts on the deterministic stocks and that the uncertainties are uncontrolled. Some additional constraints are added defining at date $t$ the possible commands $n c_t$ depending on $\xi$
The software used to manage the energy assets are usually separated into two parts. A first software, an optimization solver is used to calculate the so-called Bellman value until maturity $T$. The second one will test the Bellman values calculated during the first software run on some scenarios.

## 金融代写|随机控制理论代写STOCHASTIC CONTROL代考|Introduction and objectives

• 使用哪些热访产?
• 应该吅何管理液压闪箱?
• 执行哪些客户选顶?
• 实物投资组合应如何与末来合约对沖?
在前面的例子中，由于流动生有限的能原市场结构，对市场末来头寸的管理可以看作是对给定价格下可用能原库存的管理。 所以这个问题可以看作是一个优化问题

## 金融代写|随机控制理论代写STOCHASTIC CONTROL代考|Stochastic control optimization and simulation

$$\text { minimize } \mathbb{E}\left(\sum_{t=1}^N \phi\left(t, \xi_t, n c_t\right)\right)$$

## 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。