A Stochastic Control Approach for Constrained Stochastic Differential Games with Jumps and Regimes

We develop an approach for two-player constraint zero-sum and nonzero-sum stochastic differential games, which are modeled by Markov regime-switching jump-diffusion processes. provide the relations between a usual optimal control setting Lagrangian method. In this context, we prove corresponding theorems two different types of constraints, lead us to find real-valued Lagrange multipliers, respectively. Then, illustrate our results game problem with maximum principle technique. Our application is example cooperation bank insurance company, popular, well-known business agreement type called Bancassurance.