Bayesian modelling of the time delay between diagnosis and settlement for Critical Illness Insurance using a Burr generalised-linear-type model

Erengul Ozkok, George Streftaris, Howard R. Waters, David Wilkie

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We discuss Bayesian modelling of the delay between dates of diagnosis and settlement of claims in Critical Illness Insurance using a Burr distribution. The data are supplied by the UK Continuous Mortality Investigation and relate to claims settled in the years 1999-2005. There are non-recorded dates of diagnosis and settlement and these are included in the analysis as missing values using their posterior predictive distribution and MCMC methodology. The possible factors affecting the delay (age, sex, smoker status, policy type, benefit amount, etc.) are investigated under a Bayesian approach. A 3-parameter Burr generalised-linear-type model is fitted, where the covariates are linked to the mean of the distribution. Variable selection using Bayesian methodology to obtain the best model with different prior distribution setups for the parameters is also applied. In particular, Gibbs variable selection methods are considered, and results are confirmed using exact marginal likelihood findings and related Laplace approximations. For comparison purposes, a lognormal model is also considered. (C) 2011 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)266-279
Number of pages14
JournalInsurance: Mathematics and Economics
Volume50
Issue number2
DOIs
Publication statusPublished - Mar 2012

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