Collective risk models with dependence

Cossette, Hélène; Marceau, Étienne; Mtalai, Itre

doi:10.1016/j.insmatheco.2019.04.008

Cited by 22 publications

(21 citation statements)

References 25 publications

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“…The copula models that we present in the following subsections satisfy such an inheritance property. In contrast to ours, Cossette et al (2018)'s model does not require condition (15) to be satisfied. In terms of parameter estimation, our model and Cossette et al (2018)'s model, which have the same marginal distribution functions and copula functions, provide the same likelihood function because we always have k = n + in real observations.…”

Section: Conditional Collective Risk Modelcontrasting

confidence: 58%

“…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. While the copula is a widely used tool for modeling dependence, the choice of a suitable copula family is often a more difficult problem than the choice of a suitable marginal distribution family.…”

Section: Dependence In Collective Risk Modelsmentioning

confidence: 99%

“…Recently, researchers have relaxed those independence assumptions using flexible statistical models such as a shared random effect model (Hernández-Bastida et al, 2009;Baumgartner et al, 2015) and a copula model (Czado et al, 2012;Krämer et al, 2013;Frees et al, 2016;Cossette et al, 2018). Specifically, the copula models of Czado et al (2012) and Krämer et al (2013) introduce the dependence between frequency (N ) and average severity (M ) via a parametric copula family including a Gaussian copula; these models are also used by Frees et al (2016), Cossette et al (2018), and Lee and Shi (2019). Throughout this paper, we call (N, M ) summarized data.…”

Section: Introductionmentioning

confidence: 99%

“…For example, under a Sparre Andersen-type dependence structure, the dependence between frequency and severity is explained using the dependence between interclaim time and severity (Albrecher and Teugels, 2006;Boudreault et al, 2006;Cossette et al, 2008Cossette et al, , 2010Asimit and Badescu, 2010;Landriault et al, 2014). Recently, Liu and Wang (2017) and Cossette et al (2018) present copula models for micro-level data focusing on the structural property of the aggregate sum. However, important issues about parameter estimation and how to interpret the dependence structure have not been investigated in depth.…”

Section: Introductionmentioning

confidence: 99%

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On Copula-based Collective Risk Models

Oh,

Ahn,

Lee

2019

Preprint

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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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Section: Conditional Collective Risk Modelcontrasting

confidence: 58%

Section: Dependence In Collective Risk Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Copula-based Collective Risk Models

Oh,

Ahn,

Lee

2019

Preprint

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“…Among the early contributions, Frees et al (2014) is the first to account for dependence between the frequency and severity components, by using the frequency as an explanatory variable in the regression equation of the severity variable, and Garrido et al (2016) extended this model under the framework of exponential dispersion family. On the other hand, Czado et al (2012); Shi and Yang (2018); Cossette et al (2019); Lee and Shi (2019); Yang (2020); Oh et al (2021b) use copulas to capture the dependence between the frequency and severity components. However, so far most of the aforementioned (regression, or copula-based) models are designed for cross-sectional data only 4 .…”

Section: Introductionmentioning

confidence: 99%

A simple Bayesian state-space model for the collective risk model

Ahn¹,

Jeong²,

Lu³

2021

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The collective risk model (CRM) for frequency and severity is an important tool for retail insurance ratemaking, macro-level catastrophic risk forecasting, as well as operational risk in banking regulation. This model, which is initially designed for cross-sectional data, has recently been adapted to a longitudinal context to conduct both a priori and a posteriori ratemaking, through the introduction of random effects. However, so far, the random effect(s) is usually assumed static due to computational concerns, leading to predictive premium that omit the seniority of the claims. In this paper, we propose a new CRM model with bivariate dynamic random effect process. The model is based on Bayesian state-space models. It is associated with the simple predictive mean and closed form expression for the likelihood function, while also allowing for the dependence between the frequency and severity components. Real data application to auto insurance is proposed to show the performance of our method.

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