基于效用和均值-方差准则的多人随机微分博弈
发布时间：2019-02-19 09:25
【摘要】：以3人为例研究多人随机微分博弈,其中2人为相互合作的投资者,另一人为2投资者博弈的"虚拟"对手——金融市场.研究2种情形的随机微分博弈,一种情形为基于效用的博弈,另一种为基于均值-方差准则的博弈.对于第一种情形,2个投资者的目标是使终值财富的期望效用达到最大,金融市场的目标是使该期望效用最小.对于第二种情形,2个投资者的目标是在终值财富的期望给定时使终值财富的方差最小,金融市场的目标是使方差最大.应用随机控制理论求得2个博弈问题的最优投资策略、最优市场策略、最优值函数的显式解.通过研究,可以指导相互合作的两投资者在金融市场情况恶劣时,选择恰当的投资策略使终值财富的期望效用最大,或使自身获得一定的财富而面临的风险最小.
[Abstract]:Taking three people as an example, a multi-person stochastic differential game is studied, in which two are cooperative investors and the other is the "virtual" rival of the two-investor game, the financial market. The stochastic differential game of two cases is studied. One case is a game based on utility and the other is a game based on mean-variance criterion. In the first case, the goal of two investors is to maximize the expected utility of the final wealth, and the goal of the financial market is to minimize the expected utility. In the second case, the goal of the two investors is to minimize the variance of the final wealth when the expectation of the final wealth is given, and the goal of the financial market is to maximize the variance. By using stochastic control theory, the explicit solutions of the optimal investment strategy, optimal market strategy and optimal value function for two game problems are obtained. Through the research, we can guide the two investors who cooperate with each other to choose the appropriate investment strategy to maximize the expected utility of the final wealth or to obtain a certain amount of wealth and face the least risk when the financial market situation is bad.
【作者单位】： 西京学院理学院;
【基金】：陕西省自然科学基础研究项目(2016JM1024)
【分类号】：F830;O225
，
本文编号：2426367
[Abstract]:Taking three people as an example, a multi-person stochastic differential game is studied, in which two are cooperative investors and the other is the "virtual" rival of the two-investor game, the financial market. The stochastic differential game of two cases is studied. One case is a game based on utility and the other is a game based on mean-variance criterion. In the first case, the goal of two investors is to maximize the expected utility of the final wealth, and the goal of the financial market is to minimize the expected utility. In the second case, the goal of the two investors is to minimize the variance of the final wealth when the expectation of the final wealth is given, and the goal of the financial market is to maximize the variance. By using stochastic control theory, the explicit solutions of the optimal investment strategy, optimal market strategy and optimal value function for two game problems are obtained. Through the research, we can guide the two investors who cooperate with each other to choose the appropriate investment strategy to maximize the expected utility of the final wealth or to obtain a certain amount of wealth and face the least risk when the financial market situation is bad.
【作者单位】： 西京学院理学院;
【基金】：陕西省自然科学基础研究项目(2016JM1024)
【分类号】：F830;O225
，
本文编号：2426367
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