Bayesian estimation of finite time ruin probabilities

Resumen

We consider Bayesian inference and estimation of nite time ruin probabilities for the Sparre Andersen risk model. In practice, nite time ruin probabilities are much more useful than innite time ruin probabilities as insurance companies are usually interested in predictions for short periods of future time and not just in the limit. The dense family of Coxian distributions is considered for the approximation of both the inter-claim time and claim size distributions. The Coxian model can be well tted to real, long tailed claims data and compares well with the generalized Pareto model. Using the Coxian model for inter-claim times and claim sizes, it is possible to compute nite time ruin probabilities making use of recent results from queueing theory. We show how to obtain predictive distributions of the nite time ruin probabilities which are more informative than simple point estimations. We illustrate the procedure with simulated data and the well known Danish re loss data.