Harvesting in a Fishery with Stochastic Growth and a Mean-Reverting Price

Abstract

We analyze a continuous, nonlinear bioeconomic model to demonstrate how stochasticity in the growth of fish stocks affects the optimal exploitation policy when prices are stochastic, mean-reverting and possibly harvest dependent. Optimal exploitation has nonlinear responses to the price signal and should be conservative at low levels of biological stochasticity and aggressive at high levels. Price stochasticity induces conservative exploitation with little or no biological uncertainty, but has no strong effect when the biological uncertainty is larger. We further observe that resource exploitation should be conservative when the price reverts slowly to the mean. Simulations show that, in the long run, both the stock level and the exploitation rate are lower than in the deterministic solution. With a harvest-dependent price, the long-run price is higher in the stochastic system. The price mean reversion rate has no influence on the long-run solutions.