Thursday, November 22, 2007

Ruin and Credibility

Lourdes B. Afonso
(FCT-Universidade Nova de Lisboa)

Abstract: 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. This calculation can be approximated either through Brownian motion or a translated gamma by approximating the distribution of the aggregate claim amounts. We check the accuracy of our method by comparing the results applied to the classical risk process with those by Wikstad (1971) and Seal (1978) in finite and continuous time. We also check its accuracy in the case of exponential and mixed exponential claim amounts by choosing a very long time horizon and comparing results with exact results for infinite time ruin probability. We consider a model where the aggregate claims have a compound Poisson distribution with either a fixed or a variable Poisson parameter. Also, we consider a portfolio of risks which satisfy the assumptions of the Bühlmann credibility model, where the pure premium is updated each year in accordance with the past experience.

Notice: Note exceptional date and time
Thursday, November 22, 2007
Time: 15h00
Room: Sala Delta, Edificio Quelhas, ISEG