On an Ergodic Two-Sided Singular Control Problem

TL;DR

This paper investigates an ergodic two-sided singular control problem for one-dimensional diffusions, deriving optimal policies and rewards using the vanishing discount method, and establishing key limit results with a direct solution approach.

Contribution

It introduces a novel approach to solve ergodic two-sided singular control problems for diffusions, including explicit optimal policies and reward characterization.

Findings

Optimal reward value derived under mild conditions

Explicit optimal control policies obtained

Established Abelian and Cesàro limit results

Abstract

Motivated by applications in natural resource management, risk management, and finance, this paper is focused on an ergodic two-sided singular control problem for a general one-dimensional diffusion process. The control is given by a bounded variation process. Under some mild conditions, the optimal reward value as well as an optimal control policy are derived by the vanishing discount method. Moreover, the Abelian and Ces\`aro limits are established. Then a direct solution approach is provided at the end of the paper.