Finite Difference Computation of a Stochastic Aquaculture Problem Under Incomplete Information
Population dynamics of fishery resource is often uncertain for its manager. In most cases, especially the body growth rate is not easy to know a priori. In this paper, for approaching the issue above, a stochastic aquaculture problem under incomplete information is formulated and its associated Hamilton–Jacobi–Bellman (HJB) equation governing the value function is derived. A finite difference scheme for discretization of the HJB equation with an exponential time-stepping is then presented. The HJB equation is numerically solved with realistic parameter values for aquacultured Plecoglossus altivelis (P. altivelis, Ayu), a major inland fishery resource in Japan. The scheme naturally handles the boundary conditions and computes numerical solutions that comply with theoretical upper- and lower-bounds of the value function.
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.
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