Pricing a combined life and health insurance with level premiums and varying benefits

Abstract

The growing interest in insurance poses a threat to insurance companies. As the number of individuals seeking insurance coverage increases, the number of individuals adversely selecting the insurer also increases, which can lead to the insurance product being unprofitable. Thus, this study explores designing an insurance product – a combined life insurance and health insurance product that will reflect the actual claims of an individual to his/her policy – that will hopefully help prevent unprofitability of the insurance product. This is done by applying incentives and penalization, or the bonus-malus system, to the insurance benefit while leaving the premium constant. Assuming that premiums for life insurance and health insurance are constant, transition and pricing models are derived. Considering two forms of combination of life and health insurance: a combined life and hospitalization income insurance and a combined life and medical insurance, we illustrate the derived model assuming Makeham distribution for life insurance claims and Poisson distribution and gamma distribution for the hospitalization income insurance and medical insurance claims, respectively. The proposed design gives a new framework for combining life and health insurance, as well as a methodology for combining other types of insurances.