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Modeling and Comparing Dependencies in Multivariate Risk Portfolios

Published online by Cambridge University Press:  29 August 2014

Nicole Bäuerle  and
Alfred Müller
Nicole Bäuerle*
Affiliation:
Abteilung Mathematik VII, Operations Research, Universität Ulm
Alfred Müller*
Affiliation:
Institut für Wirtschaftstheorie, und Operations Research, Universität Karlsruhe
*
Abteilung Mathematik VII, (Operations Research), Helmholtzstr. 18, Universität Ulm, D-89069 Ulm, Germany
Institut für Wirtschaftstheorie und, Operations Research, Kaiserstr. 12, Universität Karlsruhe, D-76128 Karlsruhe, Germany
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Abstract

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In this paper we investigate multivariate risk portfolios, where the risks are dependent. By providing some natural models for risk portfolios with the same marginal distributions we are able to compare two portfolios with different dependence structure with respect to their stop-loss premiums. In particular, some comparison results for portfolios with two-point distributions are obtained. The analysis is based on the concept of the so-called supermodular ordering. We also give some numerical results which indicate that dependencies in risk portfolios can have a severe impact on the stop-loss premium. In fact, we show that the effect of dependencies can grow beyond any given bound.

Keywords

Dependent risksStop-loss premiumSupermodular orderStop-loss orderMajorizationComonotonicityExchangeable Bernoulli random variables
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 28 , Issue 1 , May 1998 , pp. 59 - 76
Copyright
Copyright © International Actuarial Association 1998

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