Double-counting problem of the bonus–malus system

Oh, Rosy; Lee, Kyung Suk; Park, Sojung C.; Ahn, Jae Youn

doi:10.1016/j.insmatheco.2020.04.008

Cited by 2 publications

(2 citation statements)

References 14 publications

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“…This approach indeed reduces to the formulas derived by Norberg (1976) in absence of a priori risk classification but the resulting optimal relativies may not minimize the expected squared difference between the true premium in the bivariate credibility model and the actual premium paid by the policyholder occupying level L in the scale, as pointed out by Tan et al (2015). See also Oh et al (2020a). The relativities minimizing the expected squared difference between the true premium and the actual premium as derived in Tan et al (2015) express in our case as…”

Section: Bonus-malus Scale With Near-claim Eventsmentioning

confidence: 86%

Bivariate Poisson Credibility Model and Bonus–Malus Scale for Claim and Near-Claim Events

Simon,

Trufin,

Denuit

2024

North American Actuarial Journal

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With the emergence of telematics, huge amounts of data have become available to insurers, raising the question of their integration into motor insurance pricing. Near-claim events are dangerous events which could have triggered a claim. Typically, they correspond to harsh deceleration, acceleration or cornering. Based on the motor third-party liability insurance portfolio of an insurance company operating in Belgium, we highlight that deceleration events are the best candidates for characterizing near-claim events. Then, we propose to integrate these events in the pricing structure in addition to policyholder's claim history with the help of a bivariate Poisson-LogNormal credibility model. Finally, we design an original bonus-malus scale based on both claim and near-claim events.

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Section: Bonus-malus Scale With Near-claim Eventsmentioning

confidence: 86%

Bivariate Poisson Credibility Model and Bonus–Malus Scale for Claim and Near-Claim Events

Simon,

Trufin,

Denuit

2024

North American Actuarial Journal

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“…More importantly, BM relativities obtained from (4), (5), and Denuit et al (2007); Tan et al (2015) are known to create some systematic bias in the prediction of premium. Such systematic bias is called the double-counting problem, and we refer interested readers to Lemaire (1995); Taylor (1997); Oh et al (2020a) for the details of the double-counting problem and its solution.…”

Section: Optimal Relativitiesmentioning

confidence: 99%

Optimal relativities in a modified Bonus-Malus system with long memory transition rules and frequency-severity dependence

Ahn,

Cheung,

et al. 2021

Preprint

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In the classical Bonus-Malus System (BMS) in automobile insurance, the premium for the next year is adjusted according to the policyholder's claim history (particularly frequency) in the previous year. Some variations of the classical BMS have been considered by taking more of driver's claim experience into account to better assess individual's risk. Nevertheless, we note that in practice it is common for a BMS to adopt transition rules according to the claim history for the past multiple years in countries such as Belgium, Italy, Korea, and Singapore. In this paper, we revisit a modified BMS which was briefly introduced in Lemaire (1995) and Pitrebois et al. (2003a). Specifically, such a BMS extends the number of Bonus-Malus (BM) levels due to an additional component in the transition rules representing the number of consecutive claim-free years. With the extended BM levels granting more reasonable bonus to careful drivers, this paper investigates the transition rules in a more rigorous manner, and provides the optimal BM relativities under various statistical model assumptions including the frequency random effect model and the dependent collective risk model. Also, numerical analysis of a real data set is provided to compare the classical BMS and our proposed BMS.

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Double-counting problem of the bonus–malus system

Cited by 2 publications

References 14 publications

Bivariate Poisson Credibility Model and Bonus–Malus Scale for Claim and Near-Claim Events

Bivariate Poisson Credibility Model and Bonus–Malus Scale for Claim and Near-Claim Events

Optimal relativities in a modified Bonus-Malus system with long memory transition rules and frequency-severity dependence

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