Financial/Actuarial Mathematics Seminar

We consider an ergodic harvesting problem with model ambiguity that arises from biology. The problem is constructed as a stochastic game with two players: the decision-maker (DM) chooses the `best' harvesting policy and an adverse player chooses the `worst' probability measure. The main result is establishing an optimal control of the DM and showing that it is a threshold policy. The optimal threshold and the optimal payoff are obtained by solving a free-boundary problem emerging from the HJB equation. As part of the proof, we fix a gap that appeared in the HJB analysis of previous papers, which analyzed the risk-neutral version of the ergodic harvesting problem. Finally, we study the dependence of the optimal threshold and the optimal payoff on the ambiguity parameter and show that if the ambiguity goes to 0, the problem converges to the risk-neutral problem. Speaker(s): Chuhao Sun (UM)