A stochastic model for critical illness insurance

Abstract

In this thesis, we present methods and results for the estimation of diagnosis inception rates for Critical Illness Insurance (CII) claims in the UK by cause. This is the first study which provides a stochastic model for the diagnosis inception rates for CII. The data are supplied by the UK Continuous Mortality Investigation and relate to claims settled in the years 1999 - 2005. First, we develop a model for the delay between dates of diagnosis and settlement of claims in CII using a generalised-lineartype model with Burr errors under both Bayesian and maximum likelihood approach. Variable selection using Bayesian methodology to obtain the best model with different prior distribution setups for the parameters is applied. For comparison purposes, a lognormal model and frequency-based model selection techniques are also considered. The non-recorded dates of diagnosis and settlement have been included in the analysis as missing values using their posterior predictive distribution and Markov Chain Monte Carlo methodology. Missing dates of diagnosis are estimated using the parsimonious claim delay distribution. With this complete data set, diagnosis inception rates for all causes (combined) and for specific causes are estimated using an appropriate claim delay distribution where the observed numbers of claim counts are assumed to have a Poisson distribution. To model the crude rates, a generalised linear model with Poisson errors and log-link function is used.