Optimal harvesting from a population in a stochastic crowded environment
Optimal harvesting from a population in a stochastic crowded environment
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DOI：
10.1016/s0025-5564(97)00029-1
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发表时间：
1997-10-01
影响因子：
4.3
通讯作者：
Oksendal, B
中科院分区：
文献类型：
--
作者：
Lungu, EM;Oksendal, B
本文研究了（Ito）随机微分方程dX（t）= rX（t）（K-Xt）dt + α X-t（K-Xt）dB（t），X-0 = x > 0作为有限承载量K > 0的随机环境中的种群增长模型.这里r和alpha是常数，B-t表示布朗运动。当r大于或等于0时，我们证明了该方程对所有x > 0都存在唯一的强整体解，并研究了它的一些性质.然后，我们考虑以下问题：什么收获策略最大化预期的总折扣量收获（整合在所有未来的时间）？我们将其表述为一个随机控制问题。然后我们证明了存在一个恒定的最优“收获触发值”x* 是（0，K）的一个元素，使得最优策略是当X-t < x* 时什么都不做，当X-t > x* 时收获X-t - x*.这导致最优种群过程X-t在x* 处向下反映。我们明确地找到x*。(C)1997年爱思唯尔科学公司
We study the (Ito) stochastic differential equationdX(t) = rX(t)(K-X,)dt + alpha X-t(K - X-t)dB(t), X-0 = x > 0as a model for population growth in a stochastic environment with finite carrying capacity K > 0. Here r and alpha are constants and B-t denotes Brownian motion. If r greater than or equal to 0, we show that this equation has a unique strong global solution for all x > 0 and we study some of its properties. Then we consider the following problem: What harvesting strategy maximizes the expected total discounted amount harvested (integrated over all future times)? We formulate this as a stochastic control problem. Then we show that there exists a constant optimal ''harvest trigger value'' x* is an element of (0, K) such that the optimal strategy is to do nothing if X-t < x* and to harvest X-t - x* if X-t > x*. This leads to an optimal population process X-t being reflected downward at x*. We find x* explicitly. (C) 1997 Elsevier Science Inc.