Fisheries management under incomplete information by optimal stochastic control and Hidden Markov Model filter

Abstract

This paper deals with mathematical modelling of strategies in harvesting of fish populations. Since too aggressive harvesting may have severe consequences, a cautious control of the process is called for. The determination of optimal harvesting based on the biomass size is made even more challenging since there is considerable uncertainty in the estimation of the stock size, the so-called incomplete information problem.Fishery management is in this paper established as an optimal control problem for a model based on nonlinear stochastic differential equations, with economic performance as objective. The so-called certainty equivalence principle, by which the estimate is used for the purposes of optimal feedback control as if it were the certain value of the state variable, is adopted. Markov controls are identified by solving the stationary Hamilton-Jacobi-Bellman equation. State estimates are obtained by a Hidden Markov Model filter, where the forward Kolmogorov equation governs the temporal evolution of estimates with the uncertain quantities. Fishery profit over time as economic performance is computed by Monte Carlo simulations, in order to compare the performances of the strategies considering control rules and precautionary approach.Two control rules in harvest policy – harvest control rule and effort control rule – are compared, with respect to their robustness given the uncertainty. The effort control rule produces a significantly higher cumulated profits, and is less sensitive to the uncertainty in stock assessment present in the system. Moreover, a precautionary approach taking the uncertainty associated with biomass estimates into account, can be achieved via quantile estimators. This approach produces an economic gain by making a more appropriately cautious decision, and leads to sustainable harvesting of fish resources.