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.We provide the relations between a usual stochastic optimal control setting and a Lagrangian method.In this context, we prove corresponding theorems for two different types of Accent Chair constraints, which lead us to find real-valued and stochastic Lagrange multipliers, respectively.Then, we illustrate our results for Egg Poachers a nonzero-sum game problem with the stochastic maximum principle technique.
Our application is an example of cooperation between a bank and an insurance company, which is a popular, well-known business agreement type called Bancassurance.