Optimal Stochastic Control with Recursive Cost Functionals of Stochastic Differential Systems Reflected in a Domain
Probability
2013-08-26 v3 Optimization and Control
Abstract
In this paper we study the optimal stochastic control problem for stochastic differential systems reflected in a domain. The cost functional is a recursive one, which is defined via generalized backward stochastic differential equations developed by Pardoux and Zhang [20]. The value function is shown to be the unique viscosity solution to the associated Hamilton-Jacobi-Bellman equation, which is a fully nonlinear parabolic partial differential equation with a nonlinear Neumann boundary condition. For this, we also prove some new estimates for stochastic differential systems reflected in a domain.
Cite
@article{arxiv.1202.1412,
title = {Optimal Stochastic Control with Recursive Cost Functionals of Stochastic Differential Systems Reflected in a Domain},
author = {Juan Li and Shanjian Tang},
journal= {arXiv preprint arXiv:1202.1412},
year = {2013}
}
Comments
24 pages