A comparative analysis of Standardized Morbidity Ratio (SMR) and Poisson-Gamma models to estimate the relative risk: Car accident insurance claims in Bandung- Indonesia
Affiliations: Department of Mathematics, Parahyangan Catholic University, Bandung 40141, Indonesia
Correspondence:
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Corresponding author: Farah Kristiani, Department of Mathematics, Parahyangan Catholic University, Gedung 9, Lantai 1, Ciumbuleuit 94, Bandung 40141, Indonesia. E-mail:farah@unpar.ac.id
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.
