Distributional Transforms, Probability Distortions, and Their Applications

被引：6

作者：

Liu, Peng ^{[1
]}

Schied, Alexander ^{[2
]}

Wang, Ruodu ^{[2
]}

机构：

[1] Univ Essex, Dept Math Sci, Colchester CO4 3SQ, Essex, England

[2] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON N2L 3G1, Canada

来源：

MATHEMATICS OF OPERATIONS RESEARCH | 2021年 / 46卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

distributional transforms; probability distortions; risk measures; option pricing; sensitivity analysis; change of measures; value-at-risk; expected shortfall; composition groups; SENSITIVITY-ANALYSIS; RISK; REPRESENTATION;

D O I：

10.1287/moor.2020.1090

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：1490 / 1512

页数：24