英文标题：
《On the Singular Control of Exchange Rates》
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作者：
Giorgio Ferrari, Tiziano Vargiolu
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最新提交年份：
2017
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英文摘要：
  Consider the problem of a central bank that wants to manage the exchange rate between its domestic currency and a foreign one. The central bank can purchase and sell the foreign currency, and each intervention on the exchange market leads to a proportional cost whose instantaneous marginal value depends on the current level of the exchange rate. The central bank aims at minimizing the total expected costs of interventions on the exchange market, plus a total expected holding cost. We formulate this problem as an infinite time-horizon stochastic control problem with controls that have paths which are locally of bounded variation. The exchange rate evolves as a general linearly controlled one-dimensional diffusion, and the two nondecreasing processes giving the minimal decomposition of a bounded-variation control model the cumulative amount of foreign currency that has been purchased and sold by the central bank. We provide a complete solution to this problem by finding the explicit expression of the value function and a complete characterization of the optimal control. At each instant of time, the optimally controlled exchange rate is kept within a band whose size is endogenously determined as part of the solution to the problem. We also study the expected exit time from the band, and the sensitivity of the width of the band with respect to the model\'s parameters in the case when the exchange rate evolves (in absence of any intervention) as an Ornstein-Uhlenbeck process, and the marginal costs of controls are constant. The techniques employed in the paper are those of the theory of singular stochastic control and of one-dimensional diffusions.
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中文摘要：
考虑一个中央银行想要管理本国货币和外国货币之间的汇率的问题。中央银行可以买卖外汇，对外汇市场的每次干预都会导致一定比例的成本，其瞬时边际价值取决于当前的汇率水平。央行的目标是将干预外汇市场的总预期成本加上总预期持有成本降到最低。我们将该问题描述为一个具有局部有界变差路径的控制的无限时域随机控制问题。汇率演变为一般线性控制的一维扩散，两个非减损过程给出了有界变化控制模型的最小分解，即中央银行已购买和出售的累计外币金额。通过找到值函数的显式表达式和最优控制的完整特征，我们为这个问题提供了一个完整的解决方案。在每个时刻，最优控制的汇率都保持在一个区间内，该区间的大小是内生确定的，这是问题解决方案的一部分。我们还研究了当汇率演变（在没有任何干预的情况下）为Ornstein-Uhlenbeck过程，且控制的边际成本不变时，预期退出时间和带宽宽度对模型参数的敏感性。本文采用的技术是奇异随机控制理论和一维扩散理论。
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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