Multi-peril frequency credibility premium via shared random effects

Jeong, Himchan; Dey, Dipak K.

doi:10.2139/ssrn.3825435

Cited by 6 publications

(5 citation statements)

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“…At this point it is worth noting that modelling positively correlated claims has been explored by many articles. See for example, Bermúdez and Karlis (2011), Bermúdez and Karlis (2012), Shi and Valdez (2014a, b), Abdallah et al (2016), Bermúdez and Karlis (2017), Bermúdez et al (2018), Bermúdez et al (2018), Pechon et al (2018), Pechon et al (2019), Bolancé and Vernic (2019), Fung et al (2019, Bolancé et al (2020), Pechon et al (2021), Jeong and Dey (2021), Gómez-Déniz and Calderín-Ojeda (2021), Tzougas and di Cerchiara (2021a, b) and Bermúdez and Karlis (2021). Finally, the proportion of zeros and kurtosis show that the marginal distributions of X 1,t , X 2,t are positively skewed and exhibit a fat-tailed structure which indicates the appropriateness of adopting a positive skewed and fat-tailed distribution (GIG distribution).…”

Section: Empirical Analysismentioning

confidence: 99%

“…At this point it is worth noting that modelling the correlation between different types of claims from the same and/or different types of coverage it is very important from a practical business standpoint. Many articles have been devoted to this topic, see for example, Bermúdez and Karlis (2011), Bermúdez and Karlis (2012), Shi and Valdez (2014a, b), Abdallah et al (2016), Bermúdez and Karlis (2017), Pechon et al (2018), Pechon et al (2019), Vernic (2019), Denuit et al (2019), Fung et al (2019), Bolancé et al (2020), Pechon et al (2021), Jeong and Dey (2021), Gómez-Déniz and Calderín-Ojeda (2021), Tzougas and di Cerchiara (2021a, b). However, with the exception of very few articles, such as Bermúdez et al (2018) and Bermúdez and Karlis (2021), the construction of bivariate INAR(1) models which can capture the serial correlation between the observations of the same policyholder over time and the correlation between different claim types remains a largely uncharted territory.…”

Section: Introductionmentioning

confidence: 99%

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Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression

2022

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In this paper, we present a novel family of multivariate mixed Poisson-Generalized Inverse Gaussian INAR(1), MMPGIG-INAR(1), regression models for modelling time series of overdispersed count response variables in a versatile manner. The statistical properties associated with the proposed family of models are discussed and we derive the joint distribution of innovations across all the sequences. Finally, for illustrative purposes different members of the MMPGIG-INAR(1) class are fitted to Local Government Property Insurance Fund data from the state of Wisconsin via maximum likelihood estimation.

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Section: Empirical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression

2022

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“…We assume that θ i ∼ G(r, 1/r) so that E[θ i ] = 1 and Var[θ i ] = 1/r. Due to the conjugacy of Poisson and gamma distributions (see Jeong & Dey, 2023), it turns out that…”

Section: Case 2a When θ I Is Randommentioning

confidence: 99%

Nonparametric intercept regularization for insurance claim frequency regression models

Lee,

Jeong

2024

Ann. actuar. sci.

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In a subgroup analysis for an actuarial problem, the goal is for the investigator to classify the policyholders into unique groups, where the claims experience within each group are made as homogenous as possible. In this paper, we illustrate how the alternating direction method of multipliers (ADMM) approach for subgroup analysis can be modified so that it can be more easily incorporated into an insurance claims analysis. We present an approach to penalize adjacent coefficients only and show how the algorithm can be implemented for fast estimation of the parameters. We present three different cases of the model, depending on the level of dependence among the different coverage groups within the data. In addition, we provide an interpretation of the credibility problem using both random effects and fixed effects, where the fixed effects approach corresponds to the ADMM approach to subgroup analysis, while the random effects approach represents the classic Bayesian approach. In an empirical study, we demonstrate how these approaches can be applied to real data using the Wisconsin Local Government Property Insurance Fund data. Our results show that the presented approach to subgroup analysis could provide a classification of the policyholders that improves the prediction accuracy of the claim frequencies in case other classifying variables are unavailable in the data.

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“…From the insurer's perspective though, bundling multiple types of insurance for the same policyholder translates into a need to develop predictive models which can efficiently capture the joint dynamics of different claims types associated with various insurance business lines. With regard to the use of alternative multivariate count models in nonlife insurance, see for instance, Abdallah et al (2016); Bermudez et al (2018); Bermudez and Karlis (2011, 2012, 2017); Bolancé et al (2020); Bolancé and Vernic (2019); Denuit et al (2019); Fung et al (2019); Gómez‐Déniz and Calderín‐Ojeda (2021); Jeong and Dey (2021); Pechon et al (2019, 2021, 2018); Shi and Valdez (2014a,b) and Tzougas and di Cerchiara (2021).…”

Section: Introductionmentioning

confidence: 99%

The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters

Tzougas

Makariou

2022

Risk Manage Insurance Review

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We introduce a multivariate Poisson-Generalized Inverse Gaussian regression model with varying dispersion and shape for modeling different types of claims and their associated counts in nonlife insurance. The multivariate Poisson-Generalized Inverse Gaussian regression model is a general class of models which, under the approach adopted herein, allows us to account for overdispersion and positive correlation between the claim count responses in a flexible manner. For expository purposes, we consider the bivariate Poisson-Generalized Inverse Gaussian with regression structures on the mean, dispersion, and shape parameters. The model's implementation is demonstrated by using bodily injury and property damage claim count data from a European motor insurer. The parameters of the model are estimated via the Expectation-Maximization algorithm which is computationally tractable and is shown to have a satisfactory performance.

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Multi-peril frequency credibility premium via shared random effects

Cited by 6 publications

References 0 publications

Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression

Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression

Nonparametric intercept regularization for insurance claim frequency regression models

The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters

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