英文标题：
《Time-consistent conditional expectation under probability distortion》
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作者：
Jin Ma, Ting-Kam Leonard Wong, Jianfeng Zhang
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最新提交年份：
2020
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英文摘要：
We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng\'s framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic setting is time-inconsistency, that is, the usual \"tower property\" fails. By localizing the probability distortion and restricting to a smaller class of random variables, we introduce a so-called distorted probability and construct a conditional expectation in such a way that it coincides with the original nonlinear expectation at time zero, but has a time-consistent dynamics in the sense that the tower property remains valid. Furthermore, we show that in the continuous time model this conditional expectation corresponds to a parabolic differential equation whose coefficient involves the law of the underlying diffusion. This work is the first step towards a new understanding of nonlinear expectations under probability distortion, and will potentially be a helpful tool for solving time-inconsistent stochastic optimization problems.
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中文摘要：
引入了概率失真条件下的条件非线性期望的新概念。这种扭曲的非线性期望通常不是次加性的，因此它超出了彭的非线性期望框架的范围。将扭曲的期望扩展到动态设置时，一个更根本的问题是时间不一致性，即通常的“塔属性”失败。通过将概率扭曲局部化并限制到一类较小的随机变量，我们引入了所谓的扭曲概率，并以这样的方式构造了一个条件期望，即它在时间零点与原始非线性期望一致，但在塔楼属性仍然有效的意义上具有时间一致的动力学。此外，我们还证明了在连续时间模型中，这个条件期望对应于一个抛物型微分方程，其系数涉及基础扩散定律。这项工作是对概率失真下非线性期望的新理解的第一步，并可能成为解决时间不一致随机优化问题的有用工具。
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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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