论文标题
由生态系统的最佳可持续利用激励的奇异随机控制问题
Singular stochastic control problems motivated by the optimal sustainable exploitation of an ecosystem
论文作者
论文摘要
我们为单调跟随器类型的单个随机控制问题提供了明确的解决方案，该问题具有（a）预期的折扣标准，（b）预期的厄贡标准，以及（c）路径悬挂的ergodic标准。这些问题是由对生态系统（例如天然渔业）的最佳可持续性开发引起的。根据对扩散系数的一般假设，折现率函数，运行收益功能和控制动作的边际利润，我们表明最佳策略是阈值类型。我们通过首先构建与其相关的HJB方程的合适解决方案来解决这三个问题，这些解决方案采用具有梯度约束的准差异不平等的形式。在沿着崇高控制问题的情况下，我们还使用合适的新变分参数。此外，我们将折现控制问题解决方案的融合到厄贡控制问题之一，因为折现率函数在亚伯利亚的意义上趋向于0。
We derive the explicit solutions to singular stochastic control problems of the monotone follower type with (a) an expected discounted criterion, (b) an expected ergodic criterion and (c) a pathwise ergodic criterion. These problems have been motivated by the optimal sustainable exploitation of an ecosystem, such as a natural fishery. Under general assumptions on the diffusion coefficients, the discounting rate function, the running payoff function and the marginal profit of control action, we show that the optimal strategies are of a threshold type. We solve the three problems by first constructing suitable solutions to their associated HJB equations, which take the form of quasi-variational inequalities with gradient constraints. In the cases of the ergodic control problems, we also use a suitable new variational argument. Furthermore, we establish the convergence of the solution of the discounted control problem to the one of the ergodic control problems as the discounting rate function tends to 0 in an Abelian sense.
