Fully nonlocal stochastic control problems with fractional Brownian motions and Poisson jumps

Abstract

In this paper, we establish a representation of mild solutions to fully nonlocal stochastic evolution problems. Through the iterative technique and energy estimates, we obtain the existence and uniqueness of mild solution. Furthermore, we prove the existence of optimal control for fully nonlocal stochastic control problems with a non-convex cost function. Two examples are given at the end.

Keywords

• fully nonlocal
• fractional brownian motion
• poisson jump
• mild solution
• optimal control