Abstract
This paper analyzes the optimal effort for a risk-averse fishermanwhere the biomass process follows a Hawkes jump-diffusion processwith Gilpin-Ayala drift. The main feature of the Hawkes process isto capture the phenomenon of clustering. The price process is of themean-reverting type. We prove a sufficient maximum principle for theoptimal control of a stochastic system consisting of an SDE drivenby the Hawkes process and, by the concavity of the Hamiltonian, weobtain the optimal effort of the fisherman for a risk-averse investor.