Relationship between MP and DPP for Risk-Sensitive Stochastic Optimal Control Problems: Viscosity Solution Framework

Abstract: In this paper, we study the relationship between general maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems, where the control domain is not necessarily convex. The original problem is equivalent to a stochastic recursive optimal control problem of a forward-backward system with quadratic generators. Relations among the adjoint processes, the generalized Hamiltonian function and the value function are proved under the framework of viscosity solutions. Some examples are given to illustrate the theoretical results.