Non-renewable Fishery Resource Management Under Incomplete Information
In this brief paper, stochastic control theory under incomplete information is applied to mathematical modeling of inland fishery management. The inland fishery resource to be managed is non-renewable in the sense that its reproduction is unsuccessful. The incomplete information comes from the uncertain body growth rate of the individuals due to temporal regime-switching of their foods. We show that finding the most cost-effective harvesting policy of the non-renewable fishery resource reduces to solving a Hamilton-Jacobi-Bellman equation. The equation is numerically solved via a simple finite difference scheme focusing on the major inland fishery resource Plecoglossusaltivelis (P. altivelis: Ayu) in Japan.
This work was supported by The River Foundation under grant The River Fund No. 285311020, The Japan Society for the Promotion Science under grant KAKENHI No. 17K15345 and No. 17J09125, and Water Resources Environment Center under grant The WEC Applied Ecology Research Grant No. 2016-02. The authors thank the officers of Hii River Fisheries Cooperatives for providing valuable data and comments for this research.