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Multirisks Model and Finite-Time Ruin Probabilities

Author

Listed:
  • Philippe Picard

    (Université de Lyon 1)

  • Claude Lefèvre

    (Université Libre de Bruxelles)

  • Ibrahim Coulibaly

    (Université Libre de Bruxelles)

Abstract

A multirisks model is constructed that describes the evolution in discrete-time of an insurance portfolio covering several interdependent risks. The main problem under study is the determination of the probabilities of ruin over a finite horizon, for one or more risks. An underlying polynomial structure in the expression of these probabilities is exhibited. This result is then used to provide a simple recursive method for their numerical evaluation. Furthermore, it is shown qualitatively that a stronger positive-type dependence between the risks increases the non-ruin probabilities. Some illustrations enhance the efficiency, in time and precision, of the developed algorithm.

Suggested Citation

  • Philippe Picard & Claude Lefèvre & Ibrahim Coulibaly, 2003. "Multirisks Model and Finite-Time Ruin Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 5(3), pages 337-353, September.
    • Handle: RePEc:spr:metcap:v:5:y:2003:i:3:d:10.1023_a:1026287204089
    DOI: 10.1023/A:1026287204089
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    References listed on IDEAS

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    1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    2. Partrat, Christian, 1994. "Compound model for two dependent kinds of claim," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 219-231, December.
    3. Sundt, Bjørn, 1999. "On Multivariate Panjer Recursions," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 29-45, May.
    4. Vernic, Raluca, 1999. "Recursive Evaluation of Some Bivariate Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 315-325, November.
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    Cited by:

    1. G. A. Delsing & M. R. H. Mandjes & P. J. C. Spreij & E. M. M. Winands, 2020. "Asymptotics and Approximations of Ruin Probabilities for Multivariate Risk Processes in a Markovian Environment," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 927-948, September.
    2. Michel Denuit & Esther Frostig & Benny Levikson, 2007. "Supermodular Comparison of Time-to-Ruin Random Vectors," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 41-54, March.
    3. Xiaohu Li & Jintang Wu & Jinsen Zhuang, 2015. "Asymptotic Multivariate Finite-time Ruin Probability with Statistically Dependent Heavy-tailed Claims," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 463-477, June.

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