Application of Generalized Linear Models in Medical Insurance Rate Making

Abstract

Generalized linear models have been used by actuaries in rate making for over the last thirty years. The basic ideas of generalized linear models were introduced by Nelder and Wedderburn in 1972. The aim of this paper is to demonstrate how Generalized linear models can be utilized in pricing private medical insurance. Private medical insurance is an indemnity based health and care insurance product that provides compensation for the cost of medical treatment. Private medical insurance will normally include outpatient and inpatient benefits and is priced on the basis of frequency multiplied by severity. The parameters of the model of frequency and model of severity are then used to estimate frequency and severity respectively. Frequency and severity increase with age and benefit limit. Females have higher frequency than males for both inpatient and outpatient benefits. Males have higher inpatient severity than females while females have higher outpatient severity than males. The pure premium has been calculated as the product of frequency and severity. The pure premium increases with age and benefit limit. The pure premium is normally loaded for commission,risk margin,expenses and profit margin to arrive at the gross premium.