Convex risk measures and the dynamics of their penalty functions

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2006-07-01 DOI:10.1524/STND.2006.24.1.61

H. Föllmer, Irina Penner

引用次数: 214

Abstract

SUMMARY We study various properties of a dynamic convex risk measure for bounded random variables which describe the discounted terminal values of financial positions. In particular we characterize time-consistency by a joint supermartingale property of the risk measure and its penalty function. Moreover we discuss the limit behavior of the risk measure in terms of asymptotic safety and of asymptotic precision, a property which may be viewed as a non-linear analogue of martingale convergence. These results are illustrated by the entropic dynamic risk measure.

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凸风险测度及其惩罚函数的动态

我们研究了描述财务状况贴现终端值的有界随机变量的动态凸风险测度的各种性质。特别地，我们通过风险测度及其惩罚函数的联合上鞅性质来表征时间一致性。此外，我们还从渐近安全性和渐近精度的角度讨论了风险测度的极限行为，这一性质可以看作是鞅收敛的非线性模拟。这些结果用熵动态风险测度来说明。

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.