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Modeling and Comparing Dependencies in Multivariate Risk Portfolios

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  • Bäuerle, Nicole
  • Müller, Alfred

Abstract

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.

Suggested Citation

  • Bäuerle, Nicole & Müller, Alfred, 1998. "Modeling and Comparing Dependencies in Multivariate Risk Portfolios," ASTIN Bulletin, Cambridge University Press, vol. 28(1), pages 59-76, May.
    • Handle: RePEc:cup:astinb:v:28:y:1998:i:01:p:59-76_01
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    Cited by:

    1. Pellerey, Franco & Shaked, Moshe & Yasaei Sekeh, Salimeh, 2012. "Comparisons of concordance in additive models," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2059-2067.
    2. Kolev, Nikolai & Paiva, Delhi, 2005. "Multinomial model for random sums," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 494-504, December.
    3. Hurlimann, W., 1999. "Non-optimality of a linear combination of proportional and non-proportional reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 219-227, May.
    4. Anastasiadis, Simon & Chukova, Stefanka, 2012. "Multivariate insurance models: An overview," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 222-227.
    5. Charpentier, A. & Segers, J.J.J., 2006. "Lower Tail Dependence for Archimedean Copulas : Characterizations and Pitfalls," Other publications TiSEM ae669e5a-1929-42d9-b137-6, Tilburg University, School of Economics and Management.

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