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Ruin Probability for Finite Erlang Mixture Claims Via Recurrence Sequences

Author

Listed:
  • Luis Rincón

    (Facultad de Ciencias UNAM México)

  • David J. Santana

    (UJAT México)

Abstract

A new procedure to find the ultimate ruin probability in the Cramér-Lundberg risk model is presented for claims with a mixture of m Erlang distributions. The method requires to solve an m order linear recurrence sequence, which translates into finding the roots of an m-th degree polynomial and solving a system of m linear equations. We here study only the case when the roots of the polynomial are simple. A new approximation method for the ruin probability is also proposed based on this procedure and the simulation of a Poisson random variable. Several analytical expressions already known for the ruin probability in the case of Erlang claims, or mixtures of these, are recovered. Numerical results and plots from R programming are provided as examples.

Suggested Citation

  • Luis Rincón & David J. Santana, 2022. "Ruin Probability for Finite Erlang Mixture Claims Via Recurrence Sequences," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 2213-2236, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09913-2
    DOI: 10.1007/s11009-021-09913-2
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    References listed on IDEAS

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