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Can a Coherent Riskmeasure be Too Subadditive?

Journal of Risk and Insurance, Vol. 75, No. 2, pp. 365-386

28 Pages Posted: 18 Mar 2009  

Jan Dhaene

Katholieke Universiteit Leuven - Faculty of Economics and Business

R. J. A. Laeven

affiliation not provided to SSRN

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Grzegorz Darkiewicz

KU Leuven - Faculty of Business and Economics (FEB)

M. J. Goovaerts

affiliation not provided to SSRN

Date Written: November 27, 2006

Abstract

We consider the problem of determining appropriate solvency capital requirements for an insurance company or a financial institution. We demonstrate that the subadditivity condition that is often imposed on solvency capital principles can lead to the undesirable situation where the shortfall risk increases by a merger. We propose to complement the subadditivity condition by a regulator's condition. We find that for an explicitly specified confidence level, the Value-at-Risk satisfies the regulator's condition and is the "most efficient" capital requirement in the sense that it minimizes some reasonable cost function. Within the class of concave distortion risk measures, of which the elements, in contrast to the Value-at-Risk, exhibit the subadditivity property, we find that, again for an explicitly specified confidence level, the Tail-Value-at-Risk is the optimal capital requirement satisfying the regulator's condition.

Keywords: risk measure, coherency, solvency, value-at-risk, subadditive

Suggested Citation

Dhaene, Jan and Laeven, R. J. A. and Vanduffel, Steven and Darkiewicz, Grzegorz and Goovaerts, M. J., Can a Coherent Riskmeasure be Too Subadditive? (November 27, 2006). Journal of Risk and Insurance, Vol. 75, No. 2, pp. 365-386. Available at SSRN: https://ssrn.com/abstract=1361925

Jan Dhaene (Contact Author)

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

Naamsestraat 69
Leuven, 3000
Belgium

R. J. A. Laeven

affiliation not provided to SSRN

Steven Vanduffel

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

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

Grzegorz Darkiewicz

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

M. J. Goovaerts

affiliation not provided to SSRN

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