Optimal control for stochastic differential delay equations with Poisson jumps and applications

Abstract

AbstractThis paper is concerned with the optimal control problem for stochastic differential delay equations with Poisson jumps, in which both state and control delays are involved. We obtain the necessary and sufficient maximum principles for the optimal control by virtue of the duality method and the anticipated backward stochastic differential equations with Poisson jumps. An optimal consumption rate problem is discussed to illustrate the applications of our results.