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Coherent Measures of Risk
Author(s) -
Artzner Philippe,
Delbaen Freddy,
Eber JeanMarc,
Heath David
Publication year - 1999
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 - 10.1111/1467-9965.00068
Subject(s) - coherent risk measure , quantile , subadditivity , risk measure , econometrics , universality (dynamical systems) , actuarial science , dynamic risk measure , expected shortfall , market risk , risk analysis (engineering) , value at risk , spectral risk measure , computer science , economics , risk management , mathematics , financial economics , business , finance , portfolio , physics , discrete mathematics , quantum mechanics
In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties “coherent.” We examine the measures of risk provided and the related actions required by SPAN, by the SEC/NASD rules, and by quantile‐based methods. We demonstrate the universality of scenario‐based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile‐based methods.