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.

本文涉及鱼类种群捕捞策略的数学建模。由于过于激进的收获可能会产生严重的后果，因此需要谨慎控制这一过程。基于生物量大小确定最佳收获变得更具挑战性，因为在估计种群大小时存在相当大的不确定性，即所谓的不完整信息问题。

在本文中，渔业管理被建立为基于非线性随机微分方程的模型的最优控制问题，以经济绩效为目标。采用所谓的确定性等价原理，根据该原理，估计值就像状态变量的某个值一样用于最优反馈控制。马尔可夫控制通过求解平稳的 Hamilton-Jacobi-Bellman 方程来确定。状态估计是通过隐马尔可夫模型滤波器获得的，其中正向 Kolmogorov 方程控制具有不确定量的估计的时间演变。通过蒙特卡罗模拟计算经济绩效随时间的渔业利润，以比较考虑控制规则和预防方法的策略的绩效。

收获政策中的两个控制规则——收获控制规则和努力控制规则——在考虑到不确定性的情况下相对于它们的稳健性进行了比较。努力控制规则产生显着更高的累积利润，并且对系统中存在的库存评估的不确定性不太敏感。此外，考虑到与生物量估计相关的不确定性的预防方法可以通过分位数估计来实现。这种方法通过做出更适当谨慎的决定来产生经济收益，并导致鱼类资源的可持续捕捞。