Entropy Coherent and Entropy Convex Measures of Risk

• 成果类型: Article
• 署名作者: Laeven, Roger J. A.; Stadje, Mitja
• 署名单位: University of Amsterdam; Tilburg University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1120.0559
• 发表日期: 2013
• 页码: 265-293
• 关键词: inf-convolution; REPRESENTATION; principles; utility

摘要

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures a risk. Entropy coherent and entropy convex measures of risk are special cases of phi-coherent and phi-convex measures of risk. Contrary to the classical use of coherent and convex measures of risk, which for a given probabilistic model entails evaluating a financial position by considering its expected loss, phi-coherent and phi-convex measures of risk evaluate a financial position under a given probabilistic model by considering its normalized expected phi-loss. We prove that (i) entropy coherent and entropy convex measures of risk are obtained by requiring phi-coherent and phi-convex measures of risk to be translation invariant; (ii) convex, entropy convex, and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic, and multiple priors preferences upon requiring the certainty equivalents to be translation invariant; and (iii) phi-convex measures of risk are certainty equivalents under variational and homothetic preferences if and only if they are convex and entropy convex measures of risk. In addition, we study the properties of entropy coherent and entropy convex measures of risk, derive their dual conjugate function, and characterize entropy coherent and entropy convex measures of risk in terms of properties of the corresponding acceptance sets.