一类生物种群投资的最优采收控制

在原有的Gauss白噪声刻画环境噪声项的基础上,考虑环境不可预知的跳跃性变化,运用Lévy白噪声建立了有界环境中的随机生物种群模型.并且,引入随机奇异控制来描述投资者的最优采收策略.进一步地,构造一族有着不同起点的控制问题,利用动态规划的思想,给出了最优采收控制问题解的充分条件,进而,将随机控制问题的求解转化为确定型偏微分方程的求解.

Optimal Harvesting Control in the Investment of a Population

In this paper,based on the existing models where the stochastic term is characterized by Gaussian white noise,we develop by Levy white noise the stochastic population equation in a crowded stochastic environment,where the unpredictable jump changes are considered. Then we introduce stochastic singular control to describe the investor＇s optimal harvesting. Furthermore,we propose a family of control problems in order to apply dynamic programming technique.And we obtain sufficient conditions for the solution of optimal harvesting control problem, where the solutions of the stochastic control problem are converted to the solutions of the deterministic partial differential equations.