Optimal relativities and transition rules of a bonus–malus system

Tan, Chong It; Li, Jackie; Li, Johnny Siu Hang; Balasooriya, Uditha

doi:10.1016/j.insmatheco.2015.02.001

Cited by 25 publications

(45 citation statements)

References 16 publications

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“…The BMS system typically constitutes three elements: the Bonus-Malus (BM) levels, transition rules to navigate the BM levels, and the relativity attached to each BM level. In the classical BMS, the transition rule is governed by frequency; it ignores the severity information, which implies that the future loss of a policyholder can be appropriately modeled by predicting the frequency only (see, e.g., Lemaire (2012); Denuit et al (2007); Tan et al (2015). In reality, this frequency-driven BMS transition rule is the standard practice in many jurisdictions.…”

Section: Introductionmentioning

confidence: 99%

Bonus-Malus premiums under the dependent frequency-severity modeling

Shi

Ahn

2019

Scandinavian Actuarial Journal

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In auto insurance, a Bonus-Malus System (BMS) is commonly used as a posteriori risk classification mechanism to set the premium for the next contract period based on a policyholder's claim history. Even though recent literature reports evidence of a significant dependence between frequency and severity, the current BMS practice is to use a frequency-based transition rule while ignoring severity information. Although Oh et al. (2019) claim that the frequencydriven BMS transition rule can accommodate the dependence between frequency and severity, their proposal is only a partial solution, as the transition rule still completely ignores the claim severity and is unable to penalize large claims. In this study, we propose to use the BMS with a transition rule based on both frequency and size of claim, based on the bivariate random effect model, which conveniently allows dependence between frequency and severity. We analytically derive the optimal relativities under the proposed BMS framework and show that the proposed BMS outperforms the existing frequency-driven BMS. Later numerical experiments are also provided using both hypothetical and actual datasets in order to assess the effect of various dependencies on the BMS risk classification and confirm our theoretical findings.

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Section: Introductionmentioning

confidence: 99%

Bonus-Malus premiums under the dependent frequency-severity modeling

Shi

Ahn

2019

Scandinavian Actuarial Journal

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“…Although there exist many variations of this type of models [21], [22], [23], most of them can be modeled by means of discrete-time Markov chains [24]. The model behind the simulator is a simple version that contains the main features of a BMS.…”

Section: A the Bms Modelmentioning

confidence: 99%

Application of a Discrete-time Markov Chain Simulation in Insurance

Morales

2015

Int. J. Recent Contrib. Eng. Sci. IT

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Abstract-This paper describes the application of an online interactive simulator of discrete-time Markov chains to an automobile insurance model. Based on the D3.js library, an interactive visual animation depicts the dynamics of individual policyholders in a bonus-malus system of automobile insurance. A survey was conducted among MSc students who used the simulator to obtain a preliminary assessment of the perceived usefulness in several dimensions of their learning process. The main findings indicate that flexible access via different devices was the most valued feature of this resource. In addition, the possibility of experimenting and simulating by means of controlling the main parameter of the model was also found to be particularly useful.

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“…Given these two inputs, the optimal relativities are determined and applied to all drivers independent of their a priori risk characteristics. To partially alleviate the unfairness towards the a priori more risky drivers, Tan et al (2015) proposed the minimisation of the objective function…”

Section: Determining Optimal Relativities Of a Bmsmentioning

confidence: 99%

“…Due to the lack of flexibility in the implementation of BMS, Pitrebois et al (2003) also argued that a single set of optimal relativities applied to all the policyholders, regardless of their a priori risk characteristics, would induce unfairness towards the drivers who are perceived to be more risky relative to the drivers that are less risky on the a priori basis. To alleviate this inadequacy scenario, Tan et al (2015) proposed a generalisation of the Norberg's criterion and analytically derived the optimal relativities under a financial equilibrium constraint first considered by Coene & Doray (1996).…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, building upon the measure of the interaction between a priori and a posteriori ratemakings developed by Pitrebois et al (2003), Tan et al (2015) suggested to quantify the different specifications of transition rules using a measure called effectiveness of transition rules. They also argued that a set of level-varying transition rules that are more flexible 1 may be more effective than the corresponding commonly adopted simple transition rules.…”

Section: Introductionmentioning

confidence: 99%

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Optimal design of a bonus-malus system: linear relativities revisited

Tan

2015

Ann. actuar. sci.

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In this paper, we revisit the determination of optimal relativities under the linear form of relativities that is more viable in designing a commercial bonus-malus system. We derive the analytical formulae for the optimal linear relativities subject to a financial balanced inequality constraint. We also numerically investigate the impact of different a priori risk classification towards the effectiveness of transition rules. Our results show that the a priori risk segmentation is not a sensitive factor for the effectiveness of transition rules. Furthermore, relative to the general relativities, we find that the restriction of linear relativities only produces a small amount of deterioration towards the numerical value of the optimised objective function.

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Optimal relativities and transition rules of a bonus–malus system

Cited by 25 publications

References 16 publications

Bonus-Malus premiums under the dependent frequency-severity modeling

Bonus-Malus premiums under the dependent frequency-severity modeling

Application of a Discrete-time Markov Chain Simulation in Insurance

Optimal design of a bonus-malus system: linear relativities revisited

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