Evaluating Transition Rules for Enhancing Fairness in Bonus–Malus Systems: An Application to the Saudi Arabian Auto Insurance Market
A Bonus–Malus System (BMS) is a ratemaking mechanism used in insurance to adjust premiums based on a policyholder’s claim history, with the goal of segmenting risk profiles more accurately. A BMS typically comprises three key components: the number of BMS levels, the transition rules dictating the m...
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MDPI AG
2025-01-01
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| author | Asrar Alyafie Corina Constantinescu Jorge Yslas |
| author_facet | Asrar Alyafie Corina Constantinescu Jorge Yslas |
| author_sort | Asrar Alyafie |
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| description | A Bonus–Malus System (BMS) is a ratemaking mechanism used in insurance to adjust premiums based on a policyholder’s claim history, with the goal of segmenting risk profiles more accurately. A BMS typically comprises three key components: the number of BMS levels, the transition rules dictating the movements of policyholders within the system, and the relativities used to determine premium adjustments. This paper explores the impact of modifications to these three elements on risk classification, assessed through the mean squared error. The model parameters are calibrated with real-world data from the Saudi auto insurance market. We begin the analysis by focusing on transition rules based solely on claim frequency, a framework in which most implemented BMSs work, including the current Saudi BMS. We then consider transition rules that depend on frequency and severity, in which higher penalties are given for large claim sizes. The results show that increasing the number of levels typically improves risk segmentation but requires balancing practical implementation constraints and that the adequate selection of the penalties is critical to enhancing fairness. Moreover, the study reveals that incorporating a severity-based penalty enhances risk differentiation, especially when there is a dependence between the claim frequency and severity. |
| format | Article |
| id | doaj-art-ac34902f654d4b74ab0d817bdc7c36dc |
| institution | Kabale University |
| issn | 2227-9091 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Risks |
| spelling | doaj-art-ac34902f654d4b74ab0d817bdc7c36dc2025-01-24T13:48:21ZengMDPI AGRisks2227-90912025-01-011311810.3390/risks13010018Evaluating Transition Rules for Enhancing Fairness in Bonus–Malus Systems: An Application to the Saudi Arabian Auto Insurance MarketAsrar Alyafie0Corina Constantinescu1Jorge Yslas2Department of Mathematical Sciences, Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZL, UKDepartment of Mathematical Sciences, Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZL, UKDepartment of Mathematical Sciences, Institute for Financial and Actuarial Mathematics, University of Liverpool, Liverpool L69 7ZL, UKA Bonus–Malus System (BMS) is a ratemaking mechanism used in insurance to adjust premiums based on a policyholder’s claim history, with the goal of segmenting risk profiles more accurately. A BMS typically comprises three key components: the number of BMS levels, the transition rules dictating the movements of policyholders within the system, and the relativities used to determine premium adjustments. This paper explores the impact of modifications to these three elements on risk classification, assessed through the mean squared error. The model parameters are calibrated with real-world data from the Saudi auto insurance market. We begin the analysis by focusing on transition rules based solely on claim frequency, a framework in which most implemented BMSs work, including the current Saudi BMS. We then consider transition rules that depend on frequency and severity, in which higher penalties are given for large claim sizes. The results show that increasing the number of levels typically improves risk segmentation but requires balancing practical implementation constraints and that the adequate selection of the penalties is critical to enhancing fairness. Moreover, the study reveals that incorporating a severity-based penalty enhances risk differentiation, especially when there is a dependence between the claim frequency and severity.https://www.mdpi.com/2227-9091/13/1/18Bonus–Malus systemoptimal relativitiestransition rulesrandom effects |
| spellingShingle | Asrar Alyafie Corina Constantinescu Jorge Yslas Evaluating Transition Rules for Enhancing Fairness in Bonus–Malus Systems: An Application to the Saudi Arabian Auto Insurance Market Risks Bonus–Malus system optimal relativities transition rules random effects |
| title | Evaluating Transition Rules for Enhancing Fairness in Bonus–Malus Systems: An Application to the Saudi Arabian Auto Insurance Market |
| title_full | Evaluating Transition Rules for Enhancing Fairness in Bonus–Malus Systems: An Application to the Saudi Arabian Auto Insurance Market |
| title_fullStr | Evaluating Transition Rules for Enhancing Fairness in Bonus–Malus Systems: An Application to the Saudi Arabian Auto Insurance Market |
| title_full_unstemmed | Evaluating Transition Rules for Enhancing Fairness in Bonus–Malus Systems: An Application to the Saudi Arabian Auto Insurance Market |
| title_short | Evaluating Transition Rules for Enhancing Fairness in Bonus–Malus Systems: An Application to the Saudi Arabian Auto Insurance Market |
| title_sort | evaluating transition rules for enhancing fairness in bonus malus systems an application to the saudi arabian auto insurance market |
| topic | Bonus–Malus system optimal relativities transition rules random effects |
| url | https://www.mdpi.com/2227-9091/13/1/18 |
| work_keys_str_mv | AT asraralyafie evaluatingtransitionrulesforenhancingfairnessinbonusmalussystemsanapplicationtothesaudiarabianautoinsurancemarket AT corinaconstantinescu evaluatingtransitionrulesforenhancingfairnessinbonusmalussystemsanapplicationtothesaudiarabianautoinsurancemarket AT jorgeyslas evaluatingtransitionrulesforenhancingfairnessinbonusmalussystemsanapplicationtothesaudiarabianautoinsurancemarket |