英文标题：
《Optimal Portfolio Liquidation in Target Zone Models and Catalytic
  Superprocesses》
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作者：
Eyal Neuman and Alexander Schied
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最新提交年份：
2015
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英文摘要：
  We study optimal buying and selling strategies in target zone models. In these models the price is modeled by a diffusion process which is reflected at one or more barriers. Such models arise for example when a currency exchange rate is kept above a certain threshold due to central bank intervention. We consider the optimal portfolio liquidation problem for an investor for whom prices are optimal at the barrier and who creates temporary price impact. This problem will be formulated as the minimization of a cost-risk functional over strategies that only trade when the price process is located at the barrier. We solve the corresponding singular stochastic control problem by means of a scaling limit of critical branching particle systems, which is known as a catalytic superprocess. In this setting the catalyst is a set of points which is given by the barriers of the price process. For the cases in which the unaffected price process is a reflected arithmetic or geometric Brownian motion with drift, we moreover give a detailed financial justification of our cost functional by means of an approximation with discrete-time models.
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中文摘要：
我们研究目标区域模型中的最优买卖策略。在这些模型中，价格是通过扩散过程建模的，扩散过程反映在一个或多个壁垒上。例如，当货币汇率由于央行干预而保持在某个阈值以上时，就会出现这种模型。我们考虑一个投资者的最优投资组合清算问题，该投资者的价格在障碍处是最优的，并且会产生暂时的价格影响。这个问题将被表述为成本风险函数的最小化，而不是仅当价格过程位于壁垒时才进行交易的策略。我们通过临界分支粒子系统的标度极限来解决相应的奇异随机控制问题，这被称为催化超过程。在这种情况下，催化剂是由价格过程中的障碍给出的一组点。对于未受影响的价格过程是带漂移的反映算术或几何布朗运动的情况，我们还通过离散时间模型的近似给出了成本函数的详细财务证明。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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