Necessary and sufficient conditions for near-optimality of stochastic delay systems

Abstract

ABSTRACTIn this paper, we study a class of near-optimisation problems with controlled systems described by the stochastic differential equations with delay. Thanks to the Ekeland's variational principle, we establish both necessary and sufficient conditions for the near-optimality of this problem by several delicate estimates for the state and adjoint processes. It is also shown that the error estimate for the near-optimality is of the order exactly. Moreover, we consider a production and consumption choice problem with delay to illustrate the application of our theoretical results.