At the end of last year, my research team got a study accepted in Environmental & Resource Economics. Our long and unsexy title — Harvesting in a Fishery with Stochastic Growth and a Mean-Reverting Price — tells only part of the story (but as much as we could fit!): We study a fish harvest model in two stochastic state variables (stock and price), where the price further is mean-reverting. Perhaps the most important finding is our demonstration of the complexity that arises in relatively simple models. The complex behavior of the optimal solution that we observe is difficult to understand intuitively, something which gave us a hard time in the peer-review process. As it should be, I guess. Anyway, our abstract reads as follows:
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.