AUT Journal of Mathematics and Computing

AUT Journal of Mathematics and Computing

Analysis of a Bayesian Additive Model for the Calibration of an Optimal Bonus-Malus System

Articles in Press

Document Type : Original Article

Authors
Ehsan Bahrami Samani 1
Saeed Mohammadpour 2
1 Shahid beheshti University, Tehran< Iran
2 Faculty of Mathematical Science, Department of Statistics, Shahid Beheshti University
10.22060/ajmc.2025.23679.1287
Abstract
The Bonus-Malus system (BMS) is a premium-setting system in which low-risk policyholders are encouraged by determining

lower premiums and high-risk are penalized by paying higher premiums. Designing a fair Bonus-Malus system is essential

for risk management. Insurance companies can attract low-risk policyholders by setting a lower premium rate and repel

high-risk policyholders by placing a higher premium. This article presents a fair optimal Bonus-Malus system for

third-party car insurance policyholders, in which insurance premiums are calculated based on the number and severity of

the policyholders' accidents and some of their characteristics. To calculate insurance premiums as fairly as possible,

this article considers Negative Binomial and Pareto distributions, respectively, for the severity and number of claims

in the form of the Bayesian additive model for location, scale, and shape (BAMLSS) structure. Then, it models how to

determine the future premiums using this structure as a Bonus-Malus system.
Keywords
Bayesian Additive Model
Risk Management
Insurance Premiums
Severity
Subjects
AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 06 September 2026