Stochastic differential game for management of non-renewable fishery resource under model ambiguity

A 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.