Optimal control of coupled forward-backward stochastic system with jumps and related Hamilton-Jacobi-Bellman equations
Abstract
In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian motion and Poisson random measure. For this end, we first study the regularity of solutions for this kind of forward-backward stochastic differential equations. We obtain that the value function is a deterministic function and satisfies the dynamic programming principle for this kind of optimal control problem. Moreover, we prove that the value functions is a viscosity solutions of the associated Hamilton-Jacobi-Bellman equations with integral-differential operators.
Keywords
Cite
@article{arxiv.1111.4642,
title = {Optimal control of coupled forward-backward stochastic system with jumps and related Hamilton-Jacobi-Bellman equations},
author = {Qian Lin},
journal= {arXiv preprint arXiv:1111.4642},
year = {2020}
}
Comments
This paper has been withdrawn by the authors due to some error in some statements