Estimasi Premi Bruto Asuransi Kendaraan Bermotor Menggunakan Metode Panjer Recursion dan Fast Fourier Transform

Sintya Putri Nugrahainy; Azizah Azizah

doi:10.37905/jjom.v7i2.32280

Estimasi Premi Bruto Asuransi Kendaraan Bermotor Menggunakan Metode Panjer Recursion dan Fast Fourier Transform

Sintya Putri Nugrahainy, Azizah Azizah

Abstract

Insurance is an agreement between two parties, namely the insurance company as the insurer and the customer as the insured. In practice, an insurance product can have hundreds or even thousands of policy contracts. This condition requires the insurer to model the compound distribution of total aggregate loss, which involves repeated convolutions. However, applying convolution to a large number of policies becomes increasingly difficult and inefficient. Therefore, alternative methods are needed to optimize the calculation process. This study uses the Panjer Recursion and Fast Fourier Transform methods to approximate the aggregate loss distribution. The model applies the Zero-Truncated Negative Binomial distribution for claim frequency and the Burr distribution for claim severity. The results show that Panjer Recursion and Fast Fourier Transform yield the same values, resulting in identical probability distributions for all values of aggregate loss. The aggregate loss distribution is then used to estimate gross premium based on the pure premium principle and the expected value principle. The loading factors increase as the confidence level rises, with θ = 3.51 at the 95% confidence level and θ = 5.47 at the 99% confidence level, resulting in total gross premiums of IDR 109,510,000 and IDR 520,835,000, respectively. The choice of confidence level plays a strategic role for insurance companies in balancing risk protection with premium affordability.

Keywords

Panjer Recursion; Fast Fourier Transform; Gross Premium; Loading Factor

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DOI: https://doi.org/10.37905/jjom.v7i2.32280