Bivariate credibility bonus–malus premiums distinguishing between two types of claims

Gómez–Déniz, Emilio

doi:10.1016/j.insmatheco.2016.06.009

Cited by 25 publications

(31 citation statements)

References 15 publications

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“…Considering the severity history in a posteriori risk classification can be traced to Picard (1976). Since then, various posteriori risk classification methods incorporating both frequency and severity history have been proposed under various collective risk models (Pinquet, 1997;Frangos and Vrontos, 2001;Hernández-Bastida et al, 2009a;Lu, 2016;Gómez-Déniz, 2016). For example, Picard (1976) and Gómez-Déniz (2016) consider a posteriori risk classification for frequency by distinguishing small and large claims with some threshold.…”

Section: Transition Rule Driven By Frequency-severity Historymentioning

confidence: 99%

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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: Transition Rule Driven By Frequency-severity Historymentioning

confidence: 99%

“…To distinguishes the degree of claim severity, we classify each claim into two types based on the claim size following Picard (1976) and Gómez-Déniz (2016). The severity with y ≤ ϕ is called a Type I claim and the severity with y > ϕ is called a Type II claim for some predetermined threshold ϕ.…”

Section: New Transition Rule: −1/ + H 1 / + H 2 Systemmentioning

confidence: 99%

Bonus-Malus premiums under the dependent frequency-severity modeling

Shi

Ahn

2019

Scandinavian Actuarial Journal

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“…In a recent work, a modification in the bonus-malus systems was proposed Gómez-Déniz (2016), which are commonly applied in automobile insurance, that differentiated between two different types of claims by including a bivariate model based on the assumption of dependence. The aforementioned work studied the impact on the bonus-malus premium in a general setting without involving individual's risk factors, such as gender, type of vehicle, area of circulation, etc.…”

Section: Introductionmentioning

confidence: 99%

A Survey of the Individual Claim Size and Other Risk Factors Using Credibility Bonus-Malus Premiums

Gómez–Déniz

Calderín–Ojeda

2020

Risks

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In this paper, a flexible count regression model based on a bivariate compound Poisson distribution is introduced in order to distinguish between different types of claims according to the claim size. Furthermore, it allows us to analyse the factors that affect the number of claims above and below a given claim size threshold in an automobile insurance portfolio. Relevant properties of this model are given. Next, a mixed regression model is derived to compute credibility bonus-malus premiums based on the individual claim size and other risk factors such as gender, type of vehicle, driving area, or age of the vehicle. Results are illustrated by using a well-known automobile insurance portfolio dataset.

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“…In Bonus-Malus systems, the premium is usually computed by using only the random variable number of claims. However, as not all the events produce the same individual claim amount Then, as different claims produce different claim sizes, it would be sensible to develop BMS based on both the number of claims and the corresponding severity (see Gómez-Déniz (2016)). In addition to this, if the severity is not included in the bounus-malus premium (BMP), the independence between the claims number and severity is implicitly assumed (see Lemaire (2004)).…”

Section: Introductionmentioning

confidence: 99%

“…In this regard, several papers have discussed the question of implementing both variables in the BMS. See, for example, Frangos and Vrontos (2001); Gómez-Déniz et al (2014) and the recent paper Gómez-Déniz (2016).…”

Section: Introductionmentioning

confidence: 99%

Multivariate Credibility in Bonus-Malus Systems Distinguishing between Different Types of Claims

Gómez–Déniz

Calderín–Ojeda

2018

Risks

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In the classical bonus-malus system the premium assigned to each policyholder is based only on the number of claims made without having into account the claims size. Thus, a policyholder who has declared a claim that results in a relatively small loss is penalised to the same extent as one who has declared a more expensive claim. Of course, this is seen unfair by many policyholders. In this paper, we study the factors that affect the number of claims in car insurance by using a trivariate discrete distribution. This approach allows us to discern between three types of claims depending wether the claims are above, between or below certain thresholds. Therefore, this model implements the two fundamental random variables in this scenario, the number of claims as well as the amount associated with them. In addition, we introduce a trivariate prior distribution conjugated with this discrete distribution that produce credibility bonus-malus premiums that satisfy appropriate traditional transition rules. A practical example based on real data is shown to examine the differences with respect to the premiums obtained under the traditional system of tarification.

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Bivariate credibility bonus–malus premiums distinguishing between two types of claims

Cited by 25 publications

References 15 publications

Bonus-Malus premiums under the dependent frequency-severity modeling

Bonus-Malus premiums under the dependent frequency-severity modeling

A Survey of the Individual Claim Size and Other Risk Factors Using Credibility Bonus-Malus Premiums

Multivariate Credibility in Bonus-Malus Systems Distinguishing between Different Types of Claims

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