Double-Counting Problem of the Bonus-Malus System
Abstract
The bonus-malus system (BMS) is a widely used premium adjustment mechanism based on policyholder's claim history. Most auto insurance BMSs assume that policyholders in the same bonus-malus (BM) level share the same a posteriori risk adjustment. This system reflects the policyholder's claim history in a relatively simple manner. However, the typical system follows a single BM scale and is known to suffer from the double-counting problem: policyholders in the high-risk classes in terms of a priori characteristics are penalized too severely (Taylor, 1997; Pitrebois et al., 2003). Thus, Pitrebois et al. (2003) proposed a new system with multiple BM scales based on the a priori characteristics. While this multiple-scale BMS removes the double-counting problem, it loses the prime benefit of simplicity. Alternatively, we argue that the double-counting problem can be viewed as an inefficiency of the optimization process. Furthermore, we show that the double-counting problem can be resolved by fully optimizing the BMS setting, but retaining the traditional BMS format.
Cite
@article{arxiv.1910.10313,
title = {Double-Counting Problem of the Bonus-Malus System},
author = {Rosy Oh and Kyung Suk Lee and Sojung C. Park and Jae Youn Ahn},
journal= {arXiv preprint arXiv:1910.10313},
year = {2019}
}