Law-invariant risk measures: Extension properties and qualitative robustness

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2014-01-14 DOI:10.1515/strm-2014-0002

Pablo Koch-Medina, Cosimo Munari

引用次数: 7

Abstract

Abstract We characterize when a convex risk measure associated to a law-invariant acceptance set in L∞ can be extended to Lp, 1≤p<∞$1\le p<\infty $ , preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concrete examples including risk measures based on expected utility, max-correlation risk measures, and distortion risk measures.

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不变风险度量:可拓性和定性稳健性

摘要刻画了L∞上与一个律不变接受集相关联的凸风险测度可以扩展到Lp, 1≤p<∞$1\le p<\infty $，并保持有限性和连续性。这个问题与相应风险度量的统计稳健性密切相关。特别注意了具体的例子，包括基于预期效用的风险度量、最大相关风险度量和扭曲风险度量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.