Bayesian estimation of ruin probability based on NHPP claim arrivals and Inverse-Gaussian distributed claim aggregates

Abstract

The purpose of this article is to estimate the ruin probability at a future time past a truncated time τ before which ruin has not occurred. It is assumed that claim arrivals are from a non-homogenous Poisson process (NHPP). The distribution of claim amount X is assumed to be heavy-tailed such as Inverse-Gaussian (IG). Gamma priors are used to find Bayes estimates of IG parameters as well as the parameter of the intensity function using an MCMC algorithm. Based on observed arrival times and claim amounts before the truncated time τ, all parameters associated with the aggregate risk process and the NHPP are estimated to compute the ruin probability. Simulation results are presented to assess the accuracy of Maximum likelihood and Bayes estimates of the ruin probability.