随机微分博弈在金融市场和石油市场上的应用

发布时间：2018-02-22 13:49

本文关键词： CEV模型 OU模型线性二次控制动态规划最优策略解合作微分博弈非合作微分博弈主从微分博弈 EAR(在险收益值)和CAR(在险资本值)　出处：《中南大学》2013年硕士论文　论文类型：学位论文

【摘要】：数理金融是用数学的方法来研究金融衍生品的新型学科,投资组合选择是其中一个重要研究课题。在现实世界中,投资者所选择的策略往往需要顾及市场上其他投资者采用的策略。在这种策略选择相互影响的环境下寻找最优策略,可视为一种博弈行为,因而可以应用博弈理论进行研究。此外,投资者在不同时间往往采用不同的策略,即投资策略是一种动态策略,因此应用随机微分博弈的理论和方法对多个投资者的动态投资决策问题进行刻画和求解无疑是一种合适的选择。本文首先在前两章中介绍了文中所要用到的基本理论和基本知识,然后在第三章中分别对股票价格服从CEV过程和OU过程的情形讨论了相应的投资组合最优化的动态微分博弈问题。应用线性二次控制和线性规划方法,得到了相应博弈问题的最优策略和最优值函数。在第四章中对石油公司之间有合作和无合作的情形,研究石油开采的博弈问题和两个寡头石油公司之间油价竞争的博弈问题。此外,考虑到石油开采存在先后次序,我们也讨论了对应的主从博弈问题。在最后一章,对上市的石油公司,采用在险收益值和在险资本值分别作为风险度量,研究了最优投资组合问题,给出了相应的最优投资组合及财富的最大期望值。
[Abstract]:Mathematical finance is a new discipline using mathematical method to study the financial derivatives, portfolio selection is one of the important research topic. In the real world, investors choose strategies often need to take into account other investors use on the market strategy in which influence environment to find the optimal strategy can be regarded as a the game behavior, which can be studied by game theory. In addition, investors often use different strategies in different time, the investment strategy is a dynamic strategy, so the application of the theory and method of stochastic differential game to describe and solve the dynamic investment decision-making problem of many investors is undoubtedly an appropriate choice.
In the beginning of the two chapter introduces the basic theory used in this paper and the basic knowledge, and then in the third chapter on the stock price follows the CEV process and OU process is discussed dynamic differential game problem portfolio optimization of the corresponding application. Two linear control and linear programming method, the optimal the optimal strategy and the corresponding game problem of value function. In the fourth chapter of the cooperation between oil companies and non cooperative situation, the price competition between the game game theory in oil exploitation and two oligarch oil company. In addition, taking into account the existence of the order of oil exploitation, we also discuss the problem of the corresponding game in the last chapter, the listed oil company, the value and value as a measure of risk capital at risk in the insurance benefits of the optimal portfolio problem, given the corresponding Optimal portfolio and the maximum expected value of wealth.

【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.9;F416.22;F224.32

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