Ruin Probability for Finite Erlang Mixture Claims Via Recurrence Sequences

Luis Rincón () and David J. Santana
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Luis Rincón: Facultad de Ciencias UNAM México
David J. Santana: UJAT México

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 2213-2236

Abstract: 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.

Keywords: Ruin probability; Cramér-Lundberg; Erlang distribution; 60E05; 97K50; 97K60 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09913-2

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