A Comparative Analysis of Standardized Morbidity Ratio (SMR) and Poisson-Gamma Models to Estimate the Relative Risk: Car Accident Insurance Claims in Bandung-Indonesia

Abstract

Insurance companies/Insurers always have a need to estimate the amount to be paid for claims filed in the future. One of the risks that should be estimated in this case, borne by car insurance companies, arises from the amount of claims for car physical damage resulting from traffic collisions. A calculating process using information of the prior number of claims from past events is required to estimate the relative risk of future claims on car accident insurance. The simplest and most common model which is usually used to estimate the relative risk is Standardized Morbidity Ratio (SMR). The estimation can also be done by using Bayesian inference, i.e.: by modelling the prior data into a distribution. One of the conjugates which is commonly applied in Bayesian approach is Poisson-Gamma. Some previous studies have estimated the relative risks of car accident insurance claims using these two models. However, the models have never been applied in Bandung municipality, one of the most populous cities in Indonesia. The models are implemented on the number of car accidents and car owners in every district in Bandung, in the year 2013 and 2014. Further, the relative risk estimations resulted from the application of the two models are mapped. From both methods, it can be concluded that Poisson-gamma model results in smoother estimation than the SMR model. It is expected that the estimated relative risk can be used by insurance companies to estimate future claims.