Stochastic Differential Portfolio Games with Regime Switching Model

Stochastic dynamic investment games with regime switching model in continuous time between two investors are developed. The market coefficients 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. A general result in optimal control for a stochastic differential game with a general payoff function is presented under some regular conditions. Use this general result to utility-based games of fixed duration, the optimal strategies and value of the games are derived explicitly.