Maximum Principles of Markov Regime-Switching Forward-Backward Stochastic Differential Equations with Jumps and Partial Information

Résumé/Abstract: In this talk, we present three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward-backward stochastic differential equations with jumps (FBSDEJs). A general sufficient maximum principle for optimal control for a system driven by a Markov regime-switching forward and backward jump-diffusion model is developed. After, an equivalent maximum principle is proved. Malliavin calculus is employed to derive a general stochastic maximum principle for non-Markovian system. The latter does not required concavity of Hamiltonian. Applications of the stochastic maximum principle to nonconcave Hamiltonian and recursive utility maximization are also discussed.