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Erlangian Approximations for Finite-Horizon Ruin Probabilities

Published online by Cambridge University Press:  29 August 2014

Soren Asmussen ,
Florin Avram  and
Miguel Usabel
Soren Asmussen
Affiliation:
Mathematical Statistics, Centre for Mathematical Sciences, Box 118, 221 00 Lund, Sweden, E-mail: asmus@maths.lth.se
Florin Avram
Affiliation:
Dept. de Math., Universite de Pau and Dept. of Actuarial Maths. & Statistics, Heriot-Watt University, Edinburgh EH14 4AS, U.K., E-mail: Florin.Avram@univ-Pau.fr
Miguel Usabel
Affiliation:
Edif. Miguel de Unamuno, Universidad Carlos III, Avda. Universidad Carlos III 22, 28270 Colmenarejo (Madrid), Spain, E-mail: usabel@emp.uc3m.es
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Abstract

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For the Cramér-Lundberg risk model with phase-type claims, it is shown that the probability of ruin before an independent phase-type time H coincides with the ruin probability in a certain Markovian fluid model and therefore has an matrix-exponential form. When H is exponential, this yields in particular a probabilistic interpretation of a recent result of Avram & Usabel. When H is Erlang, the matrix algebra takes a simple recursive form, and fixing the mean of H at T and letting the number of stages go to infinity yields a quick approximation procedure for the probability of ruin before time T. Numerical examples are given, including a combination with extrapolation.

Keywords

Erlang expirationextrapolationfinite time ruin probabilitiesfluid modelphase-type distributionssemi-Markov embedding
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 32 , Issue 2 , November 2002 , pp. 267 - 281
Copyright
Copyright © International Actuarial Association 2002

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