Investigating dependence between frequency and severity via simple generalized linear models

Lee, Woojoo; Park, Sojung C.; Ahn, Jae Youn

doi:10.1016/j.jkss.2018.07.003

Cited by 11 publications

(4 citation statements)

References 16 publications

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“…Similarly, Lee et al (2019) use automobile insurance data in Massachusetts. They find that claim severity is independent of the number of claims and only claim frequency is relevant to the number of claims in the previous period.…”

Section: Resultsmentioning

confidence: 99%

Information asymmetry, ex ante moral hazard, and uninsurable risk in liability coverage: Evidence from China's automobile insurance market

Zheng

Yao

Deng

et al. 2021

J of Risk & Insurance

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We make use of a unique data set to test for information asymmetry, as well as distinguish ex ante moral hazard from adverse selection in different types of third‐party liability claims in automobile insurance policies: that is, those with bodily injury (BI) versus those with only property damage (PD). We find that the degree of information asymmetry is higher in liability claims with BI than those with only PD. Yet, the ex ante moral hazard only exists in liability claims with PD. We use a theoretical model to propose that the difference we find between the two types of claims in ex ante moral hazard is related to uninsurable risk embedded in BI claims. We confirm this finding in another sensitivity test comparing claims from new cars and nonnew cars. Altogether, these results suggest policy reforms leading to a better pricing mechanism in the automobile insurance industry in China.

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Section: Resultsmentioning

confidence: 99%

Information asymmetry, ex ante moral hazard, and uninsurable risk in liability coverage: Evidence from China's automobile insurance market

Zheng

Yao

Deng

et al. 2021

J of Risk & Insurance

View full text Add to dashboard Cite

show abstract

“…Alternatively, one may choose a more complicated functional form of σ n as mentioned in Lee et al [2019] to consider more general dependence structures in the CRM. Depending on the purpose of the data analysis, one may use, for instance, advanced regression modeling strategies such as non-parametric regression or additive modeling; see, e.g., Hastie and Tibshirani [1990]; Faraway [2005].…”

Section: Two Part Crm For Frequency and Aggregate Severitymentioning

confidence: 99%

A copula transformation in multivariate mixed discrete-continuous models

Ahn¹,

Fuchs²,

Oh³

2020

Preprint

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Copulas allow a flexible and simultaneous modeling of complicated dependence structures together with various marginal distributions. Especially if the density function can be represented as the product of the marginal density functions and the copula density function, this leads to both an intuitive interpretation of the conditional distribution and convenient estimation procedures. However, this is no longer the case for copula models with mixed discrete and continuous marginal distributions, because the corresponding density function cannot be decomposed so nicely. In this paper, we introduce a copula transformation method that allows to represent the density function of a distribution with mixed discrete and continuous marginals as the product of the marginal probability mass/density functions and the copula density function. With the proposed method, conditional distributions can be described analytically and the computational complexity in the estimation procedure can be reduced depending on the type of copula used.

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“…One of the key assumptions frequently used in classical collective risk models is the independence of frequency and individual severities and the independence assumption among individual severities. However, recent studies (Czado et al, 2012;Krämer et al, 2013;Frees et al, 2014;Baumgartner et al, 2015;Shi et al, 2015;Garrido et al, 2016;Lee et al, 2016;Park et al, 2018;Jeong et al, 2019) have reported evidence against the independence assumption.…”

Section: Dependence In Collective Risk Modelsmentioning

confidence: 99%

“…To capture the dependence between frequency and severity or among individual severities, Hernández-Bastida et al (2009) and Baumgartner et al (2015) use a shared random effect model, and Frees et al (2014), Shi et al (2015), Garrido et al (2016), Lee et al (2016), Park et al (2018), andJeong et al (2019) use a frequency model to predict severities in the regression setting. On the contrary, Czado et al (2012), Krämer et al (2013), Frees et al (2016), Cossette et al (2018), and Lee and Shi (2019) adopt a parametric copula approach, including a Gaussian copula, to show the dependence between frequency and average severity.…”

Section: Dependence In Collective Risk Modelsmentioning

confidence: 99%

On Copula-based Collective Risk Models

Oh,

Ahn,

Lee

2019

Preprint

Self Cite

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Several collective risk models have recently been proposed by relaxing the widely used but controversial assumption of independence between claim frequency and severity. Approaches include the bivariate copula model, random effect model, and two-part frequency-severity model. This study focuses on the copula approach to develop collective risk models that allow a flexible dependence structure for frequency and severity. We first revisit the bivariate copula method for frequency and average severity. After examining the inherent difficulties of the bivariate copula model, we alternatively propose modeling the dependence of frequency and individual severities using multivariate Gaussian and t-copula functions. The proposed copula models have computational advantages and provide intuitive interpretations for the dependence structure. Our analytical findings are illustrated by analyzing automobile insurance data.

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Investigating dependence between frequency and severity via simple generalized linear models

Cited by 11 publications

References 16 publications

Information asymmetry, ex ante moral hazard, and uninsurable risk in liability coverage: Evidence from China's automobile insurance market

Information asymmetry, ex ante moral hazard, and uninsurable risk in liability coverage: Evidence from China's automobile insurance market

A copula transformation in multivariate mixed discrete-continuous models

On Copula-based Collective Risk Models

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