Numerical Solutions for Stochastic Differential Games With Regime Switching

This paper is concerned with numerical methods for stochastic differential games of regime-switching diffusions. Numerical methods using Markov chain approximation techniques are developed. A new proof of the existence of a saddle point for the stochastic differential game is provided. This new proof enables us to treat certain systems with nonseparable (in controls) structure. Convergence of the algorithms is derived by means of weak convergence methods. In addition, examples are also provided for demonstration purposes.