Optimal Ergodic Harvesting under Ambiguity

We consider an ergodic harvesting problem with model ambiguity that arises from biology. To account for the ambiguity, is constructed as a stochastic game two players: decision maker (DM) chooses “best” policy, and adverse player “worst” probability measure. The main result establishing optimal strategy (also referred to control) of DM showing it threshold policy. payoff are obtained by solving free-boundary emerging Hamilton--Jacobi--Bellman (HJB) equation. As part proof, we fix gap appeared in HJB analysis [Alvarez Hening, Stochastic Process. Appl., 2019, press], paper analyzed risk-neutral version problem. Finally, study dependence on parameter show if goes 0, converges