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.