Optimal renewable resource harvesting model using price and biomass stochastic variations: a utility based approach

Abstract

In this paper, we provide a general framework for analyzing the optimal harvest of a renewable resource (i.e. fish, shrimp) assuming that the price and biomass evolve stochastically and harvesters have a constant relative risk aversion. In order to take into account the impact of a sudden change in the environment linked to the ecosystem, we assume that the biomass are governed by a stochastic differential equation of the Gilpin–Ayala type, with regime change in the parameters of the drift and variance. Under the above assumptions, we find the optimal effort to be deployed by the collector (fishery for example) in order to maximize the expected utility of its profit function. To do this, we give the proof of the existence and uniqueness of the value function, which is derived from the Hamilton–Jacobi–Bellman equations associated with this problem, by resorting to a definition of the viscosity solution.