Bayesian modelling of the time delay between diagnosis and settlement for Critical Illness Insurance using a Burr generalised-linear-type model
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 50 (2012)
Issue (Month): 2 ()
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Web page: http://www.elsevier.com/locate/inca/505554
Bayesian analysis; Burr distribution; Critical illness insurance; Diagnosis–settlement time lag; Generalised-linear-type models; Gibbs variable selection; MCMC;
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