Analyzing Risk of Stock Collapse in a Fishery under Stochastic Profit Maximization

In commercial fisheries, stock collapse is an intrinsic problem caused by overexploitation or due to pure stochasticity. To analyze the risk of stock collapse, we apply a relatively simple Monte Carlo approach which can capture complex stock dynamics. We use an economic model with downward sloping demand and stock dependent costs. First, we derive an optimal exploitation policy as a feedback control rule and analyze the effects of stochasticity. We observe that the stochastic solution is more conservative compared to the deterministic solution at low level of stochasticity. For moderate level of stochasticity, a more myopic exploitation is optimal at small stock and conservative at large stock level. For relatively high stochasticity, one should be myopic in exploitation. Then, we simulate the system forward in time with the optimal solution. In simulated paths, some stock recovered while others collapsed. From the simulation approach, we estimate the probability of stock collapse and characterize the long term stable region.