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RECURSIVE CALCULATION OF RUIN PROBABILITIES AT OR BEFORE CLAIM INSTANTS FOR NON-IDENTICALLY DISTRIBUTED CLAIMS

Published online by Cambridge University Press:  16 December 2014

Anisoara Maria Raducan ,
Raluca Vernic  and
Gheorghita Zbaganu
Anisoara Maria Raducan
Affiliation:
Institute for Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie 13, 050711 Bucharest, Romania E-mail: anaraducan@yahoo.com
Raluca Vernic*
Affiliation:
Institute for Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie 13, 050711 Bucharest, Romania and Faculty of Mathematics and Computer Science, Ovidius University of Constanta, 124 Mamaia Blvd., 900527 Constanta, Romania
Gheorghita Zbaganu
Affiliation:
Institute for Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie 13, 050711 Bucharest, Romania and Faculty of Mathematics and Computer Science, University of Bucharest, and 14 Academiei St., 010014, Bucharest, Romania E-mail: zbagang@fmi.unibuc.ro
*
E-mail: rvernic@univ-ovidius.ro
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Abstract

In this paper, we present recursive formulae for the ruin probability at or before a certain claim arrival instant for some particular continuous time risk model. The claim number process underlying this risk model is a renewal process with either Erlang or a mixture of exponentials inter-claim times (ICTs). The claim sizes (CSs) are independent and distributed in Erlang's family, i.e., they can have different parameters, which yields a non-homogeneous risk process. We present the corresponding recursive algorithm used to evaluate the above mentioned ruin probability and we illustrate it on several numerical examples in which we vary the model's parameters to assess the impact of the non-homogeneity on the resulting ruin probability.

Keywords

Continuous time risk processruin probabilityrenewal processnon-homogeneous claim sizesErlang distributionmixture of exponentials distribution
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 45 , Issue 2 , May 2015 , pp. 421 - 443
Copyright
Copyright © ASTIN Bulletin 2014 

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