Numerical Evaluation of Continuous Time Ruin Probabilities for a Portfolio with Credebility Updated Premiums

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 Bühl mann (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.

Kewords: Probability of ruin; finite time ruin probability; credibility premiums; Bühlmann’s model; Bühlmann-Straub’s model; large portfolios; numerical evaluation.