Bayesian estimation of ruin probability based on NHPP claim arrivals and Inverse-Gaussian distributed claim aggregates. Issue 17 (9th August 2021)

• Record Type: Journal Article
• Authors: Aminzadeh, M. S.; Deng, Min
• Is Part Of: Communications in statistics. Volume 50:Issue 17(2021)
• Page Start: 4096
• Page End: 4118
• Publication Date: 2021-08-09
• Subjects: NHPP -- Inverse-Gaussian -- ruin probability -- Maximum likelihood -- Bayesian inference -- MCMC -- Mean-value function; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1710763
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: The purpose of this article is to estimate the ruin probability at a future time T τ 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 t 1, …, t n, and claim amounts x 1, …, x n 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.