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Numerical Evaluation of Continuous Time Ruin Probabilities for a Portfolio with Credibility Updated 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, ISEG and CEMAPRE, 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 and The 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

The probability of ruin in continuous and finite time is numerically evaluated in a classical risk process where the premium can be updated according to credibility models and therefore change from year to year. A major consideration in the development of this approach is that it should be easily applicable to large portfolios. Our method uses as a first tool the model developed by Afonso et al. (2009), which is quite flexible and allows premiums to change annually. We extend that model by introducing a credibility approach to experience rating.

We consider a portfolio of risks which satisfy the assumptions of the Bühlmann (1967, 1969) or Bühlmann and Straub (1970) credibility models. We compute finite time ruin probabilities for different scenarios and compare with those when a fixed premium is considered.

Keywords

Probability of ruinfinite time ruin probabilitycredibility premiumsBühlmann's modelBühlmann-Straub's modellarge portfoliosnumerical evaluation

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 399 - 414
Copyright
Copyright © International Actuarial Association 2010

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References

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