中央银行干预外汇交换市场的最优策略

Optimal Policy for the Central Bank to Intervene the Foreign Exchange Market

现汇的交换率服从几何布朗运动。中央银行的目的是使交换率尽可能限制在一个给定区域。在交换率与给定目标之间有消费成本。另外，在每一次干预中，存在一个固定成本和比例成本。目的是找一个最优干预水平和规模，使得总成本最小。可以用随机脉冲控制来解决这一问题。

A currency with exchange rate dynamics modeled as a geometric Brownian motion is considered.The objective of the Central Bank is to keep this exchange rate as close as possible to a given target,so there is a running cost associated to the difference between the exchange rate and target.Additionally,there are also fixed and proportional costs associated with each intervention.The objective is to find the optimal level,and the optimal sizes so as to minimize the total cost.We solve this problem by applying the theory of stochastic impulse controls.