随机最大值原理及其在投资组合选择和消费中的应用

发布时间：2018-01-25 13:15

本文关键词： 随机最大值原理随机微分博弈消费相对消费合作微分博弈投资组合　出处：《中南大学》2014年硕士论文　论文类型：学位论文

【摘要】：摘要：随机最大值原理是解决随机最优控制问题的一种重要方法。它是Pontryagin最大值原理的随机版本,而Pontryagin最大值原理是确定性动态系统的最优控制理论。博弈理论作为主流经济学的重要分析工具之一,其方法和思想已广泛应用于最优投资组合理论中。因此,对具有多个投资者的最优消费及投资组合博弈问题进行系统研究,具有重要的理论及现实意义。本文系统研究具有相关性扩散过程的随机最大值原理,以及在投资组合选择和消费中的应用。首先,考虑状态过程由相关布朗运动所控制的随机最大值原理,探讨随机最大值原理与动态规划原理的关系,并把得到的随机最大值原理应用于非零和主从投资组合博弈中,得到最优投资组合策略和最优值函数的显式表达式。然后利用最大值原理研究确定性财富过程和随机性财富过程下的最优消费问题,得到最优消费策略和值函数的显式表达式,并且对确定性财富过程和随机性财富过程下最优消费策略和值函数进行系统比较。最后我们研究既考虑绝对消费又考虑相对消费的最优消费博弈问题,在合作博弈与非合作博弈情形下,分别得到最优消费和值函数的显式表达式,并通过数值计算比较两种博弈情形下值函数的差别。
[Abstract]:Absrtact: stochastic maximum principle is an important method to solve stochastic optimal control problem. It is a random version of Pontryagin maximum principle. Pontryagin maximum principle is the optimal control theory of deterministic dynamic system. Game theory is one of the most important analytical tools in mainstream economics. Its methods and ideas have been widely used in the optimal portfolio theory. Therefore, it is of great theoretical and practical significance to systematically study the optimal consumption and portfolio game problem with multiple investors. In this paper, we study the stochastic maximum principle with correlation diffusion process and its application in portfolio selection and consumption. Firstly, we consider the stochastic maximum principle that the state process is controlled by the correlated Brownian motion. The relationship between the stochastic maximum principle and the dynamic programming principle is discussed, and the obtained stochastic maximum principle is applied to the non-zero sum principal and subordinate portfolio game. The explicit expressions of optimal portfolio strategy and optimal value function are obtained, and then the optimal consumption problem under deterministic wealth process and stochastic wealth process is studied by using the maximum value principle. The explicit expressions of optimal consumption strategy and value function are obtained. And the deterministic wealth process and the stochastic wealth process under the optimal consumption strategy and value function are systematically compared. Finally, we study the optimal consumption game problem considering both absolute consumption and relative consumption. In the case of cooperative game and non-cooperative game, the explicit expressions of optimal consumption and value function are obtained, and the difference of value function between the two games is compared by numerical calculation.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224.32;F830.59;F014.5

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