My research team has published a paper in the latest issue of Marine Resource Economics (vol. 30, no. 3). The paper is called Stochastically Induced Critical Depensation and Risk of Stock Collapse and discusses how stochasticity induces depensation in fisheries models. We also develop a measure of stock collapse risk and apply it to a model with an optimal harvest rate. The abstract reads as follows:
This article investigates the risk of stock collapse due to stochastically induced critical depensation in managed fisheries. We use a continuous-time surplus production model and an economic model with downwardsloping demand and stock-dependent costs. First, we derive an optimal exploitation policy as a feedback control rule by applying the Hamilton-Jacobi-Bellman approach and analyze the effects of stochasticity on the optimal policy. Then, we characterize the long-term sustainable optimal state and estimate the risk of stock collapse due to stochastically induced critical depensation. We find that the optimal harvest policy in the stochastic setting is conservative at low stochasticity and approaches the myopic solution at high stochasticity. The risk of stock collapse is increasing with the stochasticity and decreasing with stock sizes.