Relationship between General MP and DPP for the Stochastic Recursive Optimal Control Problem With Jumps: Viscosity Solution Framework

TL;DR

This paper explores the connection between the maximum principle and dynamic programming for stochastic recursive control problems with jumps, establishing relations among key processes under viscosity solution assumptions.

Contribution

It demonstrates the relationship between MP and DPP in non-convex control domains for jump processes using viscosity solutions.

Findings

Relations among adjoint processes and Hamiltonian are established.

The value function's smoothness assumption is crucial for the results.

Examples illustrate the theoretical connections.

Abstract

This paper is concerned with the relationship between general maximum principle and dynamic programming principle for the stochastic recursive optimal control problem with jumps, where the control domain is not necessarily convex. Relations among the adjoint processes, the generalized Hamiltonian function and the value function are proved, under the assumption of a smooth value function and within the framework of viscosity solutions, respectively. Some examples are given to illustrate the theoretical results.