演講者：Prof. Bernt Oksendal

單　位：Center of Mathematics for Applications, Department of Mathematics, University of Oslo

日　期：2012年2月22日　PM 14:30

地　點：國立高雄大學理學院408室

講　題：Optimal control of SPDEs with delay

摘　要：

We study optimal control problems for (time-) delayed stochastic partial differential equations with jumps. We establish sufficient and necessary (Pontryagin type) maximum principles for an optimal control of such systems. The associated adjoint processes are shown to satisfy a (time-) advanced backward stochastic partial differential equation (ABSPDE). Results on existence and uniqueness of solutions of such ABSPDEs are shown.

The results are illustrated by an application to optimal consumption from a financial or a biological system modeled by a stochastic reaction-diffusion equation with delay, and to optimal portfolio in market involving interest rate derivatives with delay.