基于随机微分博弈的最优投资

Optimal Investment Based on Stochastic Differential Game

研究存在模型风险的最优投资决策问题,将该问题刻画为投资者与自然之间的二人-零和随机微分博弈,其中自然是博弈的"虚拟"参与者.利用随机微分博弈分析方法,通过求解最优控制问题对应的HJBI(Hamilton-Jacobi-Bellman-Isaacs)方程,在完备市场和存在随机收益流的非完备市场模型下,都得到了投资者最优投资策略以及最优值函数的解析表达式.结果表明,在完备市场条件下,投资者的最优风险投资额为零,在非完备市场条件下最优投资策略将卖空风险资产,且卖空额随着随机收益流波动率的增大而增加,随风险资产波动率增大而减少.

This paper studied the problem of optimal investment with model risk via stochastic differential game approach. Suppose that nature is a ＂fictitious＂ player of game, the problem is represented as the two-player zero sum stochastic differential game between the nature and investor. Through solving HJBI equations, this paper derived the closed-form expres- sions of optimal strategies of the investor and the optimal value function under the complete market and incomplete market with stochastic income respectively via stochastic game approaches. The results indicate that the amount of optimal investment on risky asset is zero in complete market, but the amount of optimal investment on risky asset is the negative ratio between the income flow volatility and risky asset volatility in incomplete market.