Estimating the risk premium of motor insurance in Ghana using the Empirical Bayesian Credibility Theory Model

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This research explores the use of actuarial principles in estimating motor insur- ance premium for non-life insurance companies in Ghana. Unlike other countries where the business of motor insurance has developed to the level where insurance companies determine motor premiums using parameters such as the risk associ- ated with the make of the car, the distance driven within the insured period and the risk of an accident associated with the locations used by the insured, motor in- surance premiums in Ghana are determined by the regulator using a tari guide. The tari guide used by the insurance companies in Ghana is not robust and fails to consider the various risks associated with the motor insurance portfolio of the various insurance companies. The Empirical Bayesian Credibility Theory model, a non-parametric approach and the Bayesian Credibility which assumes a parametric distribution of the data were used on reported motor insurance claim amounts for 18 insurance companies in Ghana to estimate the pure premium for motor insurance. The consideration of the parametric and non-parametric cred- ibility models in estimating the risk premium of motor insurance is to establish how reliable actuarial tools can be in determining the risk premium of motor in- surance in Ghana. Using the Kolmogorov-Smirnov test at 5% level of signi cance, the distribution of reported motor insurance claim was consistent with a normal distribution. The outcome of the test of a normal prior distribution resulted in the posterior distribution also being a normal distribution and this led to the use of the Bayesian Credibility model to estimate the risk premium for motor insur- ance. The estimated risk premiums using the EBCT and the Bayesian Credibility Theory model were compared and the outcome of the two set of estimates were tested using t-test and Wilcoxon signed-rank test at 5% level of signi cance and it was established that both estimates have the same mean and follow the same distributions.
A thesis submitted to The Institute of Distance Learning, Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirements for the degree of Msc Actuarial Science,