Stochastic Differential Portfolio Games Based on Utility with Regime Switching Model

Stochastic dynamic investment games with regime switching model in continuous time between two investors are developed. The market coefficients, such as the bank interest rate, stocks appreciation rates, and volatility rates, are modulated by continuous-time Markov chain. 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. Applying the stochastic control theory, the optimal control and value functions for the problems of utility-based games are derived. Especially for CRRA case, we get the explicitly optimal control and value of the games.