论文标题
使用冲动控制的最佳现金管理
Optimal cash management using impulse control
论文作者
论文摘要
我们考虑在无限地平线下对征费过程的冲动控制，折现成本标准。我们的激励示例是现金管理问题，其中收取控制器的固定费用以及从其储备金增加或退出的比例成本，以及保留任何现金的机会成本。我们的主要结果是在这种情况下为控制带策略的最佳性提供验证定理。我们还分析了在控制带策略下受控过程的瞬态和稳态行为，并在要控制的征费过程的情况下明确求解了最佳策略，这是带有漂移和具有成倍分布的跳跃大小的复合Poisson过程的Brownian Motion的总和。
We consider the impulse control of Levy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller is charged a fixed plus proportional cost for adding to or withdrawing from his/her reserve, plus an opportunity cost for keeping any cash on hand. Our main result is to provide a verification theorem for the optimality of control band policies in this scenario. We also analyze the transient and steady-state behavior of the controlled process under control band policies and explicitly solve for the optimal policy in the case in which the Levy process to be controlled is the sum of a Brownian motion with drift and a compound Poisson process with exponentially distributed jump sizes.
