A Stochastic Maximum Principle for a Markov Regime-Switching Jump-Diffusion Model with Delay and an Application to Finance

We study a stochastic optimal control problem for a delayed Markov regime-switching jump-diffusion model. We establish necessary and sufficient maximum principles under full and partial information for such a system. We prove the existence-uniqueness theorem for the adjoint equations, which are represented by an anticipated backward stochastic differential equation with jumps and regimes. We illustrate our results by a problem of optimal consumption problem from a cash flow with delay and regimes.