Fishery management in a regime switching environment: Utility theory approach

Abstract

In this paper, we study the problem of optimal fishing for regime switching in the growth dynamics of a given fish species which is described by the differential stochastic logistic model with two states: prior or during floods and after. The resulting dynamic programming principle leads to a system of two variational inequalities. By using viscosity solutions approach, we prove the existence and uniqueness of the value functions. Then numerical approximation of the obtained system is used to determine the optimal fishing effort for a sustainable fishery.

Keywords

• Regime switching
• Crra utility
• Stochastic logistic growth
• Mean-reverting prices
• Viscosity solution
• Howard’s algorithm