Distributional Transforms, Probability Distortions, and Their Applications
本文为分布变换建立了一个通用数学框架，重点研究概率扭曲类，刻画了其满足的性质，并应用于构造风险度量及风险度量的敏感性分析，最后以期权定价为例说明概率扭曲描述测度变化。
In this paper we provide a general mathematical framework for distributional transforms, which allows for many examples that are used extensively in the literature of finance, economics, and optimization. We put a special focus on the class of probability distortions, which is a fundamental tool in decision theory. As our main results, we characterize distributional transforms satisfying various properties, and this includes an equivalent set of conditions which forces a distributional transform to be a probability distortion. As the first application, we construct new risk measures using distributional transforms. Sufficient and necessary conditions are given to ensure the convexity or coherence of the generated risk measures. In the second application, we introduce a new method for sensitivity analysis of risk measures based on composition groups of probability distortions. Finally, we construct probability distortions describing a change of measures with an example in option pricing.