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Upper stop-loss bounds for sums of possibly dependent risks with given means and variances

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  • Genest, Christian
  • Marceau, Étienne
  • Mesfioui, Mhamed

Abstract

Consider non-negative random variables X1,...,Xn whose marginal means and variances are known. The purpose of this paper is to compare two different strategies for finding an upper bound on the stop-loss premium [pi](X1+...+Xn,d)=E{max (0,X1+...+Xn-d)} that are valid for all retention amounts d[greater-or-equal, slanted]0 in the absence of information concerning the type or degree of dependence between the risks Xi. One approach consists of maximizing the premium over all possible values [rho]ij=corr(Xi,Xj), 1[less-than-or-equals, slant]i

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  • Genest, Christian & Marceau, Étienne & Mesfioui, Mhamed, 2002. "Upper stop-loss bounds for sums of possibly dependent risks with given means and variances," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 33-41, March.
    • Handle: RePEc:eee:stapro:v:57:y:2002:i:1:p:33-41
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    References listed on IDEAS

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    1. Dhaene, Jan & Goovaerts, Marc J., 1996. "Dependency of Risks and Stop-Loss Order1," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 201-212, November.
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    3. Jansen, K. & Haezendonck, J. & Goovaerts, M. J., 1986. "Upper bounds on stop-loss premiums in case of known moments up to the fourth order," Insurance: Mathematics and Economics, Elsevier, vol. 5(4), pages 315-334, October.
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    5. De Vylder, F. & Goovaerts, M. & De Pril, N., 1982. "Bounds on Modified Stop-Loss Premiums in Case of Known Mean and Variance of the Risk Variable," ASTIN Bulletin, Cambridge University Press, vol. 13(1), pages 23-36, June.
    6. Bühlmann, H. & Gagliardi, B. & Gerber, H. U. & Straub, E., 1977. "Some Inequalities for Stop-Loss Premiums," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 75-83, January.
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    Cited by:

    1. Frangos, Nikolaos & Karlis, Dimitris, 2004. "Modelling losses using an exponential-inverse Gaussian distribution," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 53-67, August.
    2. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel, 2017. "Value-at-Risk Bounds With Variance Constraints," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 923-959, September.
    3. Carole Bernard & Ludger Rüschendorf & Steven Vanduffel & Jing Yao, 2017. "How robust is the value-at-risk of credit risk portfolios?," The European Journal of Finance, Taylor & Francis Journals, vol. 23(6), pages 507-534, May.
    4. Mesfioui, Mhamed & Quessy, Jean-Francois, 2005. "Bounds on the value-at-risk for the sum of possibly dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 135-151, August.

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