Resumen de Bayesian estimation of ruin probabilities with heterogeneous and heavy-tailed insurance claim size distribution

M. Lopes Hedibert, María Concepción Ausín Olivera

• This paper describes a Bayesian approach to make inference for risk reserve processes with unknown claim size distribution. A exible model based on mix- tures of Erlang distributions is proposed to approximate the special features frequently observed in insurance claim sizes such as long tails and heteroge- neity. A Bayesian density estimation approach for the claim sizes is implemen- ted using reversible jump Markov Chain Monte Carlo methods. An advantage of the considered mixture model is that it belongs to the class of phase-type distributions and then, explicit evaluations of the ruin probabilities are possible.

  Furthermore, from a statistical point of view, the parametric structure of the mixtures of Erlang distribution o ers some advantages compared with the who- le over-parameterized family of phase-type distributions. Given the observed claim arrivals and claim sizes, we show how to estimate the ruin probabilities, as a function of the initial capital, and predictive intervals which give a measure of the uncertainty in the estimations.