Double-Counting Problem of the Bonus-Malus System

TL;DR

This paper addresses the double-counting problem in the traditional bonus-malus system for auto insurance, proposing a fully optimized solution that retains simplicity while improving risk adjustment accuracy.

Contribution

It demonstrates that the double-counting issue can be resolved through full optimization of the traditional BMS, avoiding the complexity of multiple-scale systems.

Findings

Double-counting causes over-penalization of high-risk policyholders.

Full optimization of the traditional BMS can eliminate the double-counting problem.

The proposed method maintains simplicity while improving risk adjustment.

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.