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DISTRIBUTION‐INVARIANT RISK MEASURES, INFORMATION, AND DYNAMIC CONSISTENCY
Author(s) -
Weber Stefan
Publication year - 2006
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2006.00277.x
Subject(s) - time consistency , risk measure , coherent risk measure , econometrics , dynamic risk measure , mathematics , regular polygon , consistency (knowledge bases) , spectral risk measure , invariant (physics) , axiom , probability measure , probability distribution , expected shortfall , mathematical economics , economics , actuarial science , risk management , statistics , discrete mathematics , finance , portfolio , geometry , mathematical physics
In the first part of the paper, we characterize distribution‐invariant risk measures with convex acceptance and rejection sets on the level of distributions. It is shown that these risk measures are closely related to utility‐based shortfall risk. In the second part of the paper, we provide an axiomatic characterization for distribution‐invariant dynamic risk measures of terminal payments. We prove a representation theorem and investigate the relation to static risk measures. A key insight of the paper is that dynamic consistency and the notion of “measure convex sets of probability measures” are intimately related. This result implies that under weak conditions dynamically consistent dynamic risk measures can be represented by static utility‐based shortfall risk.