Abstract
ABSTRACTA new bio-economic model for managing population of non-renewable inland fishery resource in uncertain environment is presented. Population dynamics of the resource is described with stochastic differential equations (SDEs) having ambiguous growth and mortality rates. The performance index to be maximized by the manager of the resource while minimized by nature is presented in the context of differential game theory. The dynamic programming principle leads to a Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation that governs the optimal resource management strategy under the ambiguity. The main contribution of this paper is a series of theoretical analysis on the reduced HJBI equation for non-renewable fishery resources in a broad sense, indicating that the ambiguity critically affects the resulting optimal controls. Practical implications of the theoretical analysis results are also presented focusing on artificially hatched Plecoglossus altivelis (Ayu), an important inland fishery resource in Japan.
Highlights
Fishery resources in inland waters are of importance from social, economic, ecological, and environmental viewpoints [40], and their sustainable use and conservation have been recent major concerns [12,39]
A possible way for modelling optimal control of population dynamics considering the model ambiguity is to formulate a problem based on the multiplier robust control [23,24]
The goal of the present mathematical model is to find the optimal harvesting strategy of a non-renewable fishery resource subject to stochastic population dynamics driven by a Brownian motion and a Lévy process [54], which represent different stochastic fluctuations involved in the dynamics with each other
Summary
Fishery resources in inland waters are of importance from social, economic, ecological, and environmental viewpoints [40], and their sustainable use and conservation have been recent major concerns [12,39]. A possible way for modelling optimal control of population dynamics considering the model ambiguity is to formulate a problem based on the multiplier robust control [23,24] This mathematical concept handles the model ambiguity in the context of a worstcase, min–max differential game formalism where nature controls the ambiguity. The goal of the present mathematical model is to find the optimal harvesting strategy of a non-renewable fishery resource subject to stochastic population dynamics driven by a Brownian motion and a Lévy process [54], which represent different stochastic fluctuations involved in the dynamics with each other.
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