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Conventional harvesting problems for natural resources often assumephysiological homogeneity of the body length/weight among individuals. However,such assumptions generally are not valid in real-world problems, whereheterogeneity plays an essential role in the planning of biological resourceharvesting. Furthermore, it is difficult to observe heterogeneity directly fromthe available data. This paper presents a novel optimal control framework forthe cost-efficient harvesting of biological resources for application infisheries management. The heterogeneity is incorporated into the resourcedynamics, which is the population dynamics in this case, through a probabilitydensity that can be distorted from the reality. Subsequently, the distortion,which is the model uncertainty, is penalized through a divergence, leading to anon-standard dynamic differential game wherein theHamilton-Jacobi-Bellman-Isaacs (HJBI) equation has a unique nonlinear partialdifferential term. Here, the existence and uniqueness results of the HJBIequation are presented along with an explicit monotone finite differencemethod. Finally, the proposed optimal control is applied to a harvestingproblem with recreationally, economically, and ecologically important fishspecies using collected field data.

Optimal harvesting policy for biological resources with uncertain heterogeneity for application in fisheries management