Abstract
In this article, 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 constantrelative risk aversion (CRRA) . In order to take into account the impact of a sudden change in the environ-ment linked to the ecosystem, we assume that the biomass are governed by a stochastic differential equationof the ‘Gilpin-Ayala’ type, with regime change in the parameters of the drift and variance. Under the aboveassumptions, we find the optimal effort to be deployed by the collector (fishery for example) in order tomaximize the expected utility of its profit function. To do this, we give the proof of the existence anduniqueness of the value function, which is derived from the Hamilton-Jacobi-Bellman equations associatedwith this problem, by resorting to a definition of the viscosity solution.