摘要翻译：
对于概率尺度被一般非线性函数扭曲的几何布朗运动，我们提出了一个最优停止问题。由于所涉及的Choquet集成，该问题本质上是时间不一致的。我们发展了一个新的方法，基于一个问题的重新表述，其中一个最优选择的概率分布或分位数函数停止状态。然后，可以从获得的分布/分位数函数中恢复最佳停止时间，对于几个重要的情况，可以直接的方法，或者通常通过Skorokhod嵌入。这种方法使我们能够用不同形状的收益和概率失真函数以一种相当普遍的方式解决问题。我们还讨论了结果的经济解释。特别是，我们对股票交易中广泛采用的几种平仓策略进行了论证，包括“买入并持有”、“减亏或获利”、“减亏并让获利运行”和“按历史高点百分比卖出”。
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英文标题：
《Optimal stopping under probability distortion》
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作者：
Zuo Quan Xu, Xun Yu Zhou
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最新提交年份：
2013
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分类信息：

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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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：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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英文摘要：
  We formulate an optimal stopping problem for a geometric Brownian motion where the probability scale is distorted by a general nonlinear function. The problem is inherently time inconsistent due to the Choquet integration involved. We develop a new approach, based on a reformulation of the problem where one optimally chooses the probability distribution or quantile function of the stopped state. An optimal stopping time can then be recovered from the obtained distribution/quantile function, either in a straightforward way for several important cases or in general via the Skorokhod embedding. This approach enables us to solve the problem in a fairly general manner with different shapes of the payoff and probability distortion functions. We also discuss economical interpretations of the results. In particular, we justify several liquidation strategies widely adopted in stock trading, including those of "buy and hold", "cut loss or take profit", "cut loss and let profit run" and "sell on a percentage of historical high".
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PDF链接：
https://arxiv.org/pdf/1103.1755