英文标题：
《Forward Rank-Dependent Performance Criteria: Time-Consistent Investment
  Under Probability Distortion》
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作者：
Xue Dong He and Moris S. Strub and Thaleia Zariphopoulou
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最新提交年份：
2019
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英文摘要：
  We introduce the concept of forward rank-dependent performance processes, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes, providing a bifurcation-type result. Specifically, it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the introduction of a new, distorted measure and a related market. We then build a striking correspondence between the forward rank-dependent criteria in the original market and forward criteria without probability distortions in the auxiliary market. This connection also provides a direct construction method for forward rank-dependent criteria. A byproduct of our work are some new results on the so-called dynamic utilities and on time-inconsistent problems in the classical (backward) setting.
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中文摘要：
我们引入了前向秩相关性能过程的概念，将原来的概念扩展到包含概率扭曲的前向准则。一个根本性的挑战是如何协调前向性能标准的时间一致性与概率扭曲导致的时间不一致性。为此，我们首先提出了两个不同的定义，一个基于性能值的保持，另一个基于策略的时间一致性，然后建立它们的等价性。然后，我们充分刻画了一类可行的概率失真过程，给出了一个分岔类型的结果。具体而言，要么概率扭曲在投资者永远不会投资风险资产的意义上退化，要么边际概率扭曲等于定价核分位数函数的归一化幂。我们还描述了最优财富过程，其结构促使引入一个新的、扭曲的度量和相关的市场。然后，我们在原始市场中的远期排名相关标准和辅助市场中无概率扭曲的远期标准之间建立了显著的对应关系。这种联系还为前向秩相关准则提供了一种直接构造方法。我们工作的一个副产品是关于所谓的动态效用和经典（向后）环境中的时间不一致问题的一些新结果。
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分类信息：

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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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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