Sufficient Maximum Principle for Stochastic Optimal Control Problems with General Delays

This paper is to establish a sufficient maximum principle for one kind of stochastic optimal control problem with three types of delays: a discrete delay, a moving-average delay and a noisy memory. The main features of this research include the introduction of a unified adjoint equation and a simple method to get the adjoint process. One kind of optimal consumption problem and its special cases are studied as illustrative examples, for which the adjoint equations are solved with two different approaches and the optimal consumption strategies are obtained.

Automated summary

This paper establishes a sufficient maximum principle for a stochastic optimal control problem with three types of delays, introducing a unified adjoint equation and a simple method to obtain the adjoint process. By studying an optimal consumption problem and its special cases, optimal consumption strategies are obtained through solving adjoint equations with two different approaches.