Abstract :

Aggregate loss was the total loss suffered by an insured that the insurance company had to bear in one period. Aggregate losses depend on the claim frequency and claim severity. Knowing the distribution of aggregate losses was important in calculating insurance premiums. In general, there were two types of methods for determining the distribution of aggregate losses: analytical and numerical. In this research, we discussed the application of analytic solution of aggregate loss distribution through the Laplace transform. The goodness-of-fit for claim frequency data used the Chi-square test and for claim severity data, the Kolmogorov-Smirnov test was used. The data used were secondary data from the records of PT. X in 2013, consisting of data on the claim frequency and the claim severity for insured motor vehicle insurance category 3 region 25, with claims filed being partial loss. Based on the results of the application of the analytical solution of the aggregate loss distribution, it could be concluded that the claim frequency data was Poisson distributed and the claim severity data was Lindley distributed. The probability value of someone not filing a claim was 0.7316. The expected value of the aggregate loss distribution or the average claim severity for each insured approved by the insurance companies was Rp753,533.125, and it was known that the probability of an insured not making a claim exceeding Rp2,404,433.125 is 0.7316.

 

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Keywords :

Aggregate loss, Chi-squared test, Kolmogorov-Smirnov test, Laplace transform, Partial loss.

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