On Necessary and Sufficient Conditions for Near-Optimal Singular Stochastic Controls

TL;DR

This paper establishes necessary and sufficient conditions for near-optimal singular stochastic controls in systems governed by nonlinear SDEs, extending Zhou's stochastic maximum principle using Ekeland's variational principle.

Contribution

It generalizes Zhou's stochastic maximum principle to include singular control problems with nonlinear dynamics, providing a comprehensive theoretical framework.

Findings

Derived necessary and sufficient conditions for near-optimal controls

Extended stochastic maximum principle to singular control problems

Utilized Ekeland's variational principle for proofs

Abstract

This paper is concerned with necessary and sufficient conditions for near-optimal singular stochastic controls for systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland's variational principle and some delicate estimates of the state and adjoint processes. This result is a generalization of Zhou's stochastic maximum principle for near-optimality to singular control problem.