Survival modelling approach to time to first claim and actuarial premium calculation

Akbulut, Derya
Health problems of the human beings in a society are one of the main components of the social security systems due to the dimension of the financial burden it might bring on individuals, employers, insurance companies and governments. Morbidity measures, such as incidence and prevalence of a specific disease in a certain population enable researchers to estimate for individuals the probability of being diagnosed or being prone to the diseases. This information is usually not tractable because of the non-availability of the convenient data or recordings for many countries as well as Turkey. Even if it is available, it is commonly limited with largely varying characteristics about the type and coverage of the diseases. In this regard, the pattern that a population follows for an acute disease may not be the same for chronic diseases. Having those indicators determined for a group of insureds will enable underwriters to have more profitable and economical premium calculation and precision on required reserve estimation. v Based on their characteristics such as acute or chronic behaviour, the gender, and the location of residency of people, the diseases show different behaviour on their occurrences. From the insurer‟s point of view, it is important to get to know how often the insureds visit a health institute and as a result of those visits, how large the provisions provided by insurance companies will be. Having a term like 12 months of validity on the health insurance, the occurrence of a claim due to any morbidity in the specified time span is uncertain to insurance company. Therefore, the time to first claim will be an important determinant on how many among a portfolio of N health insurance policies will cause a total claim amount of S during a year. The aim of this thesis is to investigate and determine the effect of duration elapsed to first failure as the time to first claim on the actuarial evaluation of certain morbidities. For this purpose, two different morbidities have been taken into account in order to model the time to first failure within a policy year by using survival models and find the time to first claim for determined periods in a year and its impact on actuarial premium calculation. For analyses and application purposes rheumatic heart disease (RHD) and poisoning morbidities are selected and the data of these morbidities based on some specifications, like gender, location and age are studied. Parametric and non-parametric methods are used to model the distribution of the time to first claim through distribution fitting techniques. Parametric techniques applied to the data do not give appropriate results. Therefore, non-parametric analysis namely Kaplan-Meier and life table methods are employed. The resulting survival tables for the periods of a week within a policy year are used to calculate the actuarial premium and its variance under the assumptions of individual and collective risk models. A simulation work on claim amount and frequency distributions is performed to illustrate the application of the proposed study. The results are compared with respect to the gender, location, age, and type (acute or chronic) of the morbidities for a year.


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Citation Formats
D. Akbulut, “Survival modelling approach to time to first claim and actuarial premium calculation,” M.S. - Master of Science, Middle East Technical University, 2011.