Bayesian estimation of ruin probabilities with heterogeneous and heavy-tailed insurance claim size distribution
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Bayesian estimation of ruin probabilities with heterogeneous and heavy-tailed insurance claim size distributionDate
2007-08-09Abstract
This paper describes a Bayesian approach to make inference for risk reserve processes with unknown claim size distribution. A flexible model based on mixtures of Erlang distributions is proposed to approximate the special features frequently observed in insurance claim sizes such as long tails and heterogeneity. A Bayesian density estimation approach for the claim sizes is implemented 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 others some advantages compared with the whole 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.
Keywords
Bayesian mixtures
Heavy tails
Multimodality
Phase-type distributions
Reversible jump MCMC
Risk reserve processes
Heavy tails
Multimodality
Phase-type distributions
Reversible jump MCMC
Risk reserve processes