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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
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

Afonso, L.B. (2008) Evaluation of ruin probabilities forsurplus processes with credibility and surplus dependent premiums. PhD thesis, ISEG, Lisbon.Google Scholar
Afonso, L.B., Egídio Dos Reis, A.D. and Waters, H.R. (2009) Calculating continuous time ruin probabilities for a large portfolio with varying premiums. ASTIN Bulletin, 39(1), 117–136.Google Scholar
Asmussen, S. (1999) On the ruin problem for some adapted premium rules, MaPhySto Research Report No.5. University of Aarhus, Denmark. Available at http://www.maphysto.dk/publications/MPS-RR/1999/5.pdf. Google Scholar
Bühlmann, H. (1967) Experience rating and credibility. ASTIN Bulletin, 4(3), 199–207.Google Scholar
Bühlmann, H. (1969) Experience rating and credibility. ASTIN Bulletin, 5(2), 157–165.Google Scholar
Bühlmann, H. and Gisler, A. (2005) A Course in Credibility Theory and its Applications, Springer, Berlin.Google Scholar
Bühlmann, H. and Straub, E. (1970) Glaubwürdigkeit für Schadensätze, Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker, 1970, 111–133. Translated to English by Brooks, C.E. “Credibility for Loss Ratios” ARCH, 1972.Google Scholar
Daykin, C.D., Pentikäinen, T. and Pesonen, M. (1996) Practical Risk Theory for Actuaries. Chapman and Hall, London.Google Scholar
Dubey, A. (1977) Probabilité de ruine lorsque le paramètre de Poisson est ajusté a posteriori, Mitteilungender Vereinigung Schweizerischer Versicherungsmathematiker, 77, 131–141.Google Scholar
Norberg, R. (1979) The credibility approach to experience rating, Scandinavian Actuarial Journal, 1979, 181–221.Google Scholar
Trufin, J. and Loisel, S. (2009) Ultimate ruin probability in discrete time with Bühlmann credibility premium adjustments, Working paper. Available at http://hal.archives-ouvertes.fr/hal-00426790/en/. Google Scholar
Tsai, C. and Parker, G. (2004) Ruin probabilities: classical versus credibility, 2004 NTU International Conference on Finance.Google Scholar