We consider a finite time horizon optimal stochastic control problem for a system of stochastic functional differential equations with a bounded memory. Under some sufficiently smooth conditions, a Hamilton-Jacobi-Bellman (HJB) equation for the value function of the optimal control problem is derived. It is shown that the value function is the unique viscosity solution of the HJB equation. In addition, as a special case, we will study a portfolio optimization problem in which there is some delayed information. An explicit solution is derived under certain conditions. ( Slides)
Speaker: Tao Pang, North Carolina State Univ.