The determination of the aggregate loss distribution through the numerical inverse of the characteristic function using the trapezoidal quadrature rule

Abstract

Aggregate loss is the total loss suffered by an insured in a certain period. The aggregate loss depends on the claim frequency and the amount of the claim each time the insured makes a claim. The distribution of aggregate losses must be known to calculate motor vehicle insurance premiums. In general, there are two methods that can be used in determining the distribution of aggregate losses, namely exact and numerical. When an exact solution is difficult to find, numerical methods such as Monte Carlo, Panjer Recursion, and Fast Fourier Transform can be used. This research will discuss the determination of the distribution of aggregate losses through the numerical inverse of the characteristic function using the trapezoidal quadrature rule, on the data of motor vehicle insurance category 7 in Indonesia. The estimated cumulative distribution function for the largest aggregate loss is 0.999993. When x=0, it means that if someone does not file a claim, the estimated value of the cumulative distribution function is 0.9293. This value is close to the percentage of the number of insured, which is 0.9241.