Harvesting of a stochastic population under a mixed regular-singular control formulation

TL;DR

This paper develops a mixed regular-singular control model for optimal harvesting and renewing a stochastic population, analyzing properties of the value function, its limits, and providing numerical strategies for implementation.

Contribution

It introduces a novel control formulation with regime-switching and state constraints for stochastic population management, including analysis of the limiting behavior and numerical approximation methods.

Findings

Value functions exhibit specific properties under the control model.

The limiting value function as noise intensity increases is characterized.

Numerical methods effectively approximate optimal strategies.

Abstract

This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime-switching is introduced. The decision-makers either harvest or renew with finite or infinite harvesting/renewing rates. The payoff functions depend on the harvesting/renewing rates. Several properties of the value functions are established. The limiting value function as the white noise intensity approaches infinity is identified. The Markov chain approximation method is used to find a numerical approximation of the value function and optimal strategies.