Bonus-Malus Premium for Third Party Liability Insurance with Poisson-Lindley Distribution Claim Frequency and Exponential-Inverse Gamma Distribution Claim Severity

Bilqis Nur  Rizkia; Aceng Komarudin  Mutaqin

doi:10.36456/jstat.vol18.no1.a10327

Authors

Bilqis Nur Rizkia Universitas Islam Bandung
Aceng Komarudin Mutaqin Universitas Islam Bandung

DOI:

https://doi.org/10.36456/jstat.vol18.no1.a10327

Keywords:

Bonus-Malus, Third Party Liability Insurance, Poisson-Lindley and Exponential-Inverse Gamma Distributions

Abstract

Insurance is a form of mutual cooperation that provides protection against unforeseen risks. With insurance, individuals can feel more secure about potential future losses, whether related to themselves or their property. As the number of motor vehicles in Indonesia increases, so does the risk of traffic accidents, making motor vehicle insurance particularly Third Party Liability (TPL) insurance increasingly important. To enhance fairness, insurance companies implement premium systems based on claim history, one of which is the bonus-malus system. This study discusses premium calculation in a bonus-malus system for TPL insurance, assuming that claim frequency follows a Poisson-Lindley distribution and claim severity follows an exponential-inverse gamma distribution. The data used are secondary data obtained from PT. XYZ for the 2019 underwriting year, focusing on policyholders in category two. The analysis results indicate that the selected distributions fit the data well. The optimal bonus-malus system determines that the initial pure premium to be paid by new policyholders is Rp22,970. Premiums in subsequent years are adjusted based on claim activity: increasing if a claim is made and decreasing if no claim occurs.

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