Stochastic Optimal Control and Linear Programming Approach

• DOI: 10.1007/s00245-010-9120-y
• Publication Date: 2010-10-14T03:33:27Z
• Authors: R. Buckdahn; D. Goreac; M. Quincampoix
• Keywords: Stochastic game; Stochastic control; Hamilton–Jacobi equation; Viscosity solution; Hamilton–Jacobi–Bellman equation

We study a classical stochastic optimal control problem with constraints and discounted payoff in an infinite horizon setting. The main result of the present paper lies in the fact that this optimal control problem is shown to have the same value as a linear optimization problem stated on some appropriate space of probability measures. This enables one to derive a dual formulation that appears to be strongly connected to the notion of (viscosity sub) solution to a suitable Hamilton-Jacobi-Bellman equation. We also discuss relation with long-time average problems.