An optimal control problem for functional forward-backward stochastic systems and related Path-dependent HJB equations
Probability
2013-01-03 v3 Optimization and Control
Abstract
In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming principle and the related Path-dependent Hamilton-Jacobi-Bellman (HJB) equation in the framework of functional It\^o calculus. The stochastic verification theorem for the smooth case is proved. Finally, we show that the value function is the viscosity solution of the Path-dependent HJB equation.
Cite
@article{arxiv.1204.6543,
title = {An optimal control problem for functional forward-backward stochastic systems and related Path-dependent HJB equations},
author = {Shaolin Ji and Shuzhen Yang},
journal= {arXiv preprint arXiv:1204.6543},
year = {2013}
}
Comments
We need to make a major change of this paper