|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.