Abstract
The problem of irreversibly harvesting from a general one dimensional (Wiener-Poisson) jump diffusion population model is studied. For a wide class of models, including stochastic generalizations of the logistic model earlier studied by Lungu & Øksendal (1997) and Alvarez & Shepp (1998), the optimal strategy is a downwards local time reflection at a trigger level x*. Both these works find that this trigger level is higher than of the corresponding deterministic problem; we show that this property depends crucially upon the uncertainty being Brownian. Furthermore, we give conditions under which jump uncertainty also increases x* compared to the deterministic model.