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Radhiah, Radhiah
Prodi Pend. Bahasa Indonesia, FKIP Universitas Malikussaleh
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Journal : Jurnal Matematika UNAND

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Optimal Bonus-Malus Premium with the Claim Frequency Distribution is Negative Binomial and the Claim Severity Distribution is Truncated Weibull Maulidi, Ikhsan; MAULIDIA, IZZAH; Radhiah, Radhiah; Apriliani, Vina
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.179-195.2026

Abstract

The optimal bonus-malus system is a system for determining the amount of premium in the next period based on the frequency and severity of claims filed by policyholders in the previous period. In this article, we study the insurance premium formula using the optimal bonus-malus system with the claim frequency has a negative binomial distribution and the claim severity has a truncated Weibull distribution. The method to derive the bonus-malus formula uses a Bayes solution with a quadratic loss function. The formula obtained has been also applied to the data of motor vehicle insurance to calculate the risk premium that must be paid by the policyholder. From the calculation results, the insurance premiums that use the optimal bonus-malus system with a truncated Weibull distribution are more profitable for both the company and the insurer than the Weibull distribution.
Co-Authors Abdul Azis Acha, Basyarudin Aina, Nandatul Aiyub Septian Al Anshari Andri Yusman Persada Anisa, Fahra Aprilia Putri, Kartika Ariska, Raja Novi Asda Asda Beby Aulia Pradita Cahyono, Rizqi Dara Rahmatillah Dea Riski Dewi Larasati, Dewi Emilda, Emilda Fadlon Haser, Teuku Fadly, Fahmy Fahmy Fadly Fakhrah Fakhrah, Fakhrah Fauzan . Fazriani, Nurafni Febri, Suri Purnama Hafiza, Nurul Hanisah Hanisah Hanisah, Hanisah Harahap, Antoni Harliyana, Iba Harliyana, Iba Hasannuddin, Teuku Haser, Teuku Fadlon Herlina Putri Endah Sari Hidayatsyah Hidayatsyah Hutabarat, Krismonita Darliani Iba Harliyana Idaryani Idaryani Ika Rezvani Aprita Ikhsan Maulidi indra, siti balqies Juni Ahyar Juwita, Afrina Kartika Aprilia Putri Kartika Aprilia Putri Lestari, Netia Mahsa, Masithah Maimun Maimun Maisarah Maisarah, Maisarah Marzuki Maulidawati Maulidawati Maulidi, Ikhsan MAULIDIA, IZZAH Muhammad Aidil Akbar Muhammad Iqbal Muhammad Syahroni Nazaruddin Novi Hardiana Putri Novita Sari Nurhaliza Nurhaliza Nurhasanah Bancin Nurjannah Nurjannah Nurjannah Nurmaida Nurmaida Persada, Andri Yusman Pratiwi, Rani Ardesi Purnama Febri, Suri Putri, Kartika Aprilia Rahma Zuhra Rani Ardesi Pratiwi Rasyimah Rasyimah Reza Pahlevi Ginting Ririn Rahayu Ririn Rahayu Rita Zahara Rozalina Rozalina Safriandi Safriandi Safriandi Safriandi Safriandi Safriandi, Safriandi Safriandi, Safriandi Sarbaini Satriadi Satriadi siregar, putri Siti Balqies Indra Siti Nurhaliza Sudirman Sudirman Suri Purnama Febri Syahriandi Syahriandi Syardiansah, Syardiansah Tarmizi Usman Teuku Fadlon Haser Teuku Fadlon Haser Ulza Maramis Vina Apriliani Wahyu Isnanda Nasution Wulanda Yusman Persada, Andri Zulfan Zulfitri Zulfitri