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Dependent discrete risk processes –calculation of the probability of ruin

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  • Stanislaw Heilpern

    () (Department of Statistics, Wroclaw University of Economics)

Abstract

This paper is devoted to discrete processes of dependent risks. The random variables describing the time between claims can be dependent in such processes, unlike under the classical approach. The ruin problem is investigated and the probability of ruin is computed. The relation between the degree of dependence and the probability of ruin is studied. Three cases are presented. Different methods of characterizing the dependency structure are examined. First, strictly dependent times between claims are investigated. Next, the dependency structure is described using an Archimedean copula or using Markov chains. In the last case, three situations in which the probability of ruin can be exactly computed are presented. Numerical examples in which the claims have a geometric distribution are investigated. A regular relation between the probability of ruin and the degree of dependence is only observed in the Markov chain case.

Suggested Citation

  • Stanislaw Heilpern, 2010. "Dependent discrete risk processes –calculation of the probability of ruin," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 2, pages 59-76.
  • Handle: RePEc:wut:journl:v:2:y:2010:p:59-76
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    References listed on IDEAS

    as
    1. Dickson, David C.M. & dos Reis, Alfredo D. Egídio & Waters, Howard R., 1995. "Some Stable Algorithms in Ruin Theory and Their Applications," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 25(02), pages 153-175, November.
    2. Gerber, Hans U., 1988. "Mathematical Fun with the Compound Binomial Process," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 18(02), pages 161-168, November.
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