Finite Difference Computation of a Stochastic Aquaculture Problem Under Incomplete Information

机译：信息不完全的随机水产养殖问题的有限差分计算

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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.

机译：渔业资源的种群动态对其管理者而言通常是不确定的。在大多数情况下，尤其是人体生长率不容易先验地知道。为了解决上述问题，本文提出了信息不完全的随机水产养殖问题，并推导了与之相关的控制价值函数的汉密尔顿-雅各比-贝尔曼（HJB）方程。然后提出了一种采用指数时间步长离散化HJB方程的有限差分方案。 HJB方程使用日本主要内陆渔业资源水产假单胞菌（P. altivelis，Ayu）的实际参数值进行数值求解。该方案自然处理边界条件，并计算符合值函数理论上限和下限的数值解。

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《Finite difference methods: theory and applications》|2018年|638-645|共8页
会议地点 Lozenetz(BG)
作者
Hidekazu Yoshioka; Kentaro Tsugihashi; Yuta Yaegashi;
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Faculty of Life and Environmental Science, Shimane University, Nishikawatsu-cho 1060, Matsue 690-8504, Japan;

Graduate School of Life and Environmental Science, Shimane University, Nishikawatsu-cho 1060, Matsue 690-8504, Japan;

Graduate School of Agriculture, Kyoto University, Kitashirakawa-oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan,Research Fellow of Japan Society for the Promotion of Science, Tokyo, Japan;

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Finite Difference Computation of a Stochastic Aquaculture Problem Under Incomplete Information

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