Long-Term Average Impulse and Singular Control of a Growth Model with Two Revenue Sources

TL;DR

This paper provides explicit solutions for long-term average impulse and singular control problems in a diffusion process, with applications in resource management and finance.

Contribution

It introduces a unified approach to solving long-term average impulse and singular control problems with explicit solutions and sensitivity analysis.

Findings

Explicit solutions for impulse control problems are derived.

Connections between impulse and singular control are established.

Sensitivity analysis highlights parameter impacts on optimal policies.

Abstract

This paper analyzes and explicitly solves a class of long-term average impulse control problems and a related class of singular control problems. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The model is motivated by applications such as the optimal long-term management of renewable resources and financial portfolio management. A large class of admissible policies is identified over which the agent seeks to maximize her long-term average reward, consisting of a running reward and income from either discrete impulses or singular actions. In addition to the long-term average objective, we will briefly consider the long-term expected total reward functional and its relation to overtaking optimality. Sensitivity analysis with regard to the parameters of the impulse control model are performed. Key connections between the impulse and singular control problems are displayed.