Model and parameter uncertainty in critical illness insurance

Critical illness (CI) insurance involves cover that pays out on the diagnosis of an illness which is deemed to be critical. Estimation and graduation of CI insurance claim rates has been challenging, partly because of the diagnosis of the insured event often being unclear or not recorded. This introduces additional uncertainties in the evaluation of claim rates. In this work, which was funded by an Institute and Faculty of Actuaries research grant, we have addressed the issue of model and parameter uncertainty in claim rate estimation, when the date of diagnosis is missing, aiming at obtaining graduated rates that can be applied to estimate the future cash flow of CI policies and determine insurers' liability more accurately. Better understanding of uncertainty in rate graduation and pricing is important for insurers, not least because of future changes in the interpretation of the " definition" of an illness or advances in medical practice leading to more efficient diagnosis and treatment. Estimation of claim rates was addressed in this project using a parametric Poisson model for the number of claims, which accounts for claims that have not been settled by the end of the observation. This was achieved by considering probabilities of the distribution of the delay period between diagnosis of insured illness and settlement of the corresponding claim. We have developed appropriate generalised-linear-type models (including lognormal, Burr, generalised gamma and generalised beta) to investigate this delay, using data supplied by the Continuous Mortality Investigation (1999-2005). The analysis includes various claim risk factors (e. g. gender, benefit amount, policy duration and so on) and was performed under a Bayesian framework, using Markov chain Monte Carlo estimation techniques. Based on this experience, our analysis suggests that estimates of the claim delay distribution are model sensitive, but claim rates and pricing are not. Under the best claim delay distribution fitting, the following risk factors are considered important for predictive purposes: policy duration, selling office, benefit type, benefit amount, policy type and cause of claim.