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Zainul Muttaqin
Universitas Hamzanwadi
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Stability and Fairness of Premiums in Bonus–Malus Systems Based on a Premium Change Index Lili Hernawati; Zainul Muttaqin; Eli Zulkatri; Putri Amalia; Alvianus Kristian Sumual
Khatulistiwa: Jurnal Pendidikan dan Sosial Humaniora Vol. 6 No. 2 (2026): Juni: Khatulistiwa: Jurnal Pendidikan dan Sosial Humaniora
Publisher : AMIK Veteran Purwokerto

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55606/khatulistiwa.v6i2.11249

Abstract

The bonus–malus system is a premium adjustment mechanism in insurance that links the level of premiums to the claim history of policyholders. In practice, such a system is expected to reflect risk in a fair manner while maintaining premium stability over time. However, studies addressing premium stability and fairness often remain implicit and lack clear quantitative indicators. This study aims to analyze premium stability and fairness in a bonus–malus system using a premium change index as an evaluation tool. The research adopts an evaluative and descriptive approach based on a table of relative bonus–malus premiums defined by the total number of claims, the number of large claims, and the bonus–malus period. Premium stability is assessed through inter-period premium changes, which are formalized into the Stability–Fairness Premium Index (SFPI) defined as the average absolute change in premiums over time. The results show that the index increases with the total number of claims, indicating a higher sensitivity of premiums to risk exposure. Nevertheless, for a fixed total number of claims, the index is not affected by the number of large claims, suggesting that penalties are applied proportionally without increasing premium volatility. These findings indicate that the analyzed bonus–malus system achieves a balance between premium stability and fairness. The proposed index provides a simple and transparent quantitative framework for evaluating bonus–malus systems and may support the development of fairer and more stable premium-setting policies in insurance.
Co-Authors Almas Salsabila Alvianus Kristian Sumual Amaliana MZ, Zulfiana ANDI WIJAYA Andika Dutha Bachari Anggraini Dwi Cahya Arman, Rolly Aulia, Riza Azima, Pauzan Azizah, Dinda Noor Azmussya’ni Baiq Rismarini Nursaly Dwiyanto, Muhammad Alvin Eli Zulkatri Eva Nurmayani Hadi, Erwin Hafiz, Alwan Hapipi Hapipi Hardianti, Wiwin Haris Widita Heru Pratikno Heryono, Heri Hidayatul Hamdiah I Gede Palgunadi Iradhatullah Rahim Irawan, Helmi Hendra Irfan, Moh Jamil Jamil Jumhur Jumhur Khalisatun, Khalisatun Khalisatun, Khalisatun Lalu Fakihuddin Lalu Masud Lenny Nofriyani Adam Lili Hernawati M, Muhana Nurkhalishah Maryani, Intan Muh Taufiq Muh. Jaelani Al Pansori Muh. Ridwan Markarma Muh. Taufiq Muh. Tauiq Mu’awanah Mu’awanah Nurdiansyah, Urai Pratama, Fauzan Novaldy Pristianingrum, Santy Puspita, Fergy Desy Putri Amalia Riyana Rizki Yuliatin Roni Amrulloh S Gunawan Sari, Hasrina Satrya HD, Dharma Shiyabuddin, Shiyabuddin Simanjuntak, Cindy Uli Natalia Siswahyudianto Soewignjo Soemohardjo Sudana, Dadang Suherman, Suherman Syamsiar Zamzam Syihabuddin Syihabuddin Taufiq, Muh. Titin Ernawati Wenny Astuti A Wijaya, Herman Zainiati, Baiq Lely