This talk deals with optimal harvesting strategies for the predator in a predator-prey system. The objective function is of long-run average per unit time type in the path-wise sense.
The ecological system is subject to environmental noise modeled as stochastic differential equations driven by a Brownian motion. The main result is to prove the existence and uniqueness of solutions to the .Hamilton–Jacobi–Bellman equation associated with the controlled stochastic system.
The existence of optimal Markov strategies is also derived.