The necessary and sufficient conditions for stochastic differential systems with multi-time states cost functional

TL;DR

This paper develops a stochastic maximum principle for control systems with multi-time states cost functionals, providing necessary and sufficient conditions for optimality and exploring related constrained and near-optimal control problems.

Contribution

It introduces a new optimal control framework with multi-time states cost functional and derives the corresponding maximum principle and optimality conditions.

Findings

Established stochastic maximum principle for multi-time states control systems

Derived necessary and sufficient optimality conditions

Explored constrained and near-optimal control problems

Abstract

From economics point of view, we investigate a new optimal control problem driven by a stochastic differential equation with a multi-time states cost functional. By constructing a series of first-order adjoint equations, we establish the stochastic maximum principle and sufficient optimality conditions for this new optimal control problem. A constraints problem also be studied. In the end, we develop a near optimal control problem for a general cost functional.