CIR框架下的投资组合效用微分博弈

建立了Cox-Ingersoll—Ross随机利率下的关于两个投资者的投资组合效用微分博弈模型．市场利率具有CIR动力，博弈双方存在唯一的损益函数，损益函数取决于投资者的投资组合财富．一方选择动态投资组合策略以最大化损益函数，而另一方则最小化损益函数．运用随机控制理论，在一般的效用函数下得到了基于效用的博弈双方的最优策略．特别考虑了常数相对风险厌恶情形，获得了显示的最优投资组合策略和博弈值．最后给出了数值例子和仿真结果以说明本文的结论．

Utility-based Differential Game for Portfolio in CIR Framework

Utility-based differential game for portfolio with Cox-Ingersoll-Ross （CIR） stochastic interest rate in continuous time between two investors is developed. The market interest rate has the dynamics of CIR interest rate. The prices of risky stocks are affected by CIR interest rate. There is a single payoff function which depends on both investors＇ wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff, while his opponent is simultaneously choosing a dynamic portfolio strategy so as to minimize the same quantity. The optimal strategies for the utility-based game are obtained by the stochastic control theory. Especially for the constant relative risk aversion utility game with fixed duration, the explicit optimal strategies and value of the game are derived. The numerical example and simulation are provided to illustrate the results obtained in this paper.