Abstract

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.

Keywords

Coherent risk measureQuantileSubadditivityRisk measureEconometricsUniversality (dynamical systems)Actuarial scienceDynamic risk measureExpected shortfallMarket riskRisk analysis (engineering)Value at riskSpectral risk measureComputer scienceEconomicsRisk managementMathematicsFinancial economicsBusinessFinance

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Publication Info

Year
1999
Type
article
Volume
9
Issue
3
Pages
203-228
Citations
8812
Access
Closed

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Cite This

Philippe Artzner, Freddy Delbaen, Jean‐Marc Eber et al. (1999). Coherent Measures of Risk. Mathematical Finance , 9 (3) , 203-228. https://doi.org/10.1111/1467-9965.00068

Identifiers

DOI
10.1111/1467-9965.00068