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Calculating Continuous Time Ruin Probabilities for a Large Portfolio with Varying Premiums

Published online by Cambridge University Press:  09 August 2013

Lourdes B. Afonso ,
Alfredo D. Egídio dos Reis  and
Howard R. Waters
Lourdes B. Afonso
Affiliation:
Depart. de Matemática and CMA, Faculdade Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal, E-mail: lbafonso@fct.unl.pt
Alfredo D. Egídio dos Reis
Affiliation:
Depart. of Mathematics, CEMAPRE and ISEG, Technical University of Lisbon, Rua do Quelhas 6, 1200-781 Lisboa, Portugal, E-mail: alfredo@iseg.utl.pt
Howard R. Waters
Affiliation:
Depart. of Actuarial Mathematics and Statistics andThe Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton Edinburgh EH14 4AS, Scotland, E-mail: H.R.Waters@ma.hw.ac.uk
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Abstract

In this paper we present a method for the numerical evaluation of the ruin probability in continuous and finite time for a classical risk process where the premium can change from year to year. A major consideration in the development of this methodology is that it should be easily applicable to large portfolios. Our method is based on the simulation of the annual aggregate claims and then on the calculation of the ruin probability for a given surplus at the start and at the end of each year. We calculate the within-year ruin probability assuming a translated gamma distribution approximation for aggregate claim amounts.

We illustrate our method by studying the case where the premium at the start of each year is a function of the surplus level at that time or at an earlier time.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 1 , May 2009 , pp. 117 - 136
Copyright
Copyright © International Actuarial Association 2009

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