Risk Measures and Comonotonicity: A Review

Stochastic Models, Vol. 22, pp. 573-606, 2006

34 Pages Posted: 11 Mar 2009 Last revised: 17 Mar 2009

Jan Dhaene

Katholieke Universiteit Leuven - Faculty of Economics and Business

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Qihe Tang

University of Amsterdam - Amsterdam School of Economics (ASE)

M. J. Goovaerts

affiliation not provided to SSRN

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE)

David Vyncke

Ghent University-Universiteit Gent - Department of Applied Mathematics and Computer Science

Date Written: 2006

Abstract

In this paper we examine and summarize properties of several well-known risk measures that can be used in the framework of setting solvency capital requirements for a risky business. Special attention is given to the class of (concave) distortion risk measures. We investigate the relationship between these risk measures and theories of choice under risk. Furthermore we consider the problem of how to evaluate risk measures for sums of non-independent random variables. Approximations for such sums, based on the concept of comonotonicity, are proposed. Several examples are provided to illustrate properties or to prove that certain properties do not hold. Although the paper contains several new results, it is written as an overview and pedagogical introduction to the subject of risk measurement. The paper is an extended version of Dhaene et al. (2003).

Keywords: risk measures, coherency, CTE

Suggested Citation

Dhaene, Jan and Vanduffel, Steven and Tang, Qihe and Goovaerts, M. J. and Kaas, Rob and Vyncke, David, Risk Measures and Comonotonicity: A Review (2006). Available at SSRN: https://ssrn.com/abstract=892185

Jan Dhaene (Contact Author)

Katholieke Universiteit Leuven - Faculty of Economics and Business ( email )

Naamsestraat 69
Leuven, 3000
Belgium

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

Qihe Tang

University of Amsterdam - Amsterdam School of Economics (ASE) ( email )

Roetersstraat 11
Amsterdam, North Holland 1018 WB
Netherlands

M. J. Goovaerts

affiliation not provided to SSRN

Rob Kaas

University of Amsterdam - Faculty of Economics & Econometrics (FEE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

David Vyncke

Ghent University-Universiteit Gent - Department of Applied Mathematics and Computer Science ( email )

Gent, 9000
Belgium

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