Testing for Random Effects in Compound Risk Models via Bregman Divergence

Jeong, Himchan

doi:10.1017/asb.2020.19

Cited by 14 publications

(6 citation statements)

References 30 publications

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“…which has been shown in actuarial literature including, but not limited to, Frangos and Vrontos (2001), Jeong (2020), and Jeong and Valdez (2020). While use of the aforementioned Poisson-gamma model allows us to evaluate the individual predictive premium for a large portfolio at ease and naturally captures possible overdispersion, such a model cannot reflect the possibility of zero-inflation in claim frequency.…”

Section: Claim Frequency Model With Longitudinality and Zero-inflationmentioning

confidence: 99%

Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach

Kim

Jeong

Dey

2022

Risks

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While both zero-inflation and the unobserved heterogeneity in risks are prevalent issues in modeling insurance claim counts, determination of Bayesian credibility premium of the claim counts with these features are often demanding due to high computational costs associated with a use of MCMC. This article explores a way to approximate credibility premium for claims frequency that follows a zero-inflated Poisson distribution via variational Bayes approach. Unlike many existing industry benchmarks, the proposed method enables insurance companies to capture both zero-inflation and unobserved heterogeneity of policyholders simultaneously with modest computation costs. A simulation study and an empirical analysis using the LGPIF dataset were conducted and it turned out that the proposed method outperforms many industry benchmarks in terms of prediction performances and computation time. Such results support the applicability of the proposed method in the posterior ratemaking practices.

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Section: Claim Frequency Model With Longitudinality and Zero-inflationmentioning

confidence: 99%

Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach

Kim

Jeong

Dey

2022

Risks

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“…0 are estimated by maximizing the joint likelihood. Note that this is equivalent to the static credibility premium in Jeong and Valdez (2020b) and Jeong (2020). In order to assure E θ…”

Section: Empirical Analysismentioning

confidence: 99%

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

Ahn¹,

Jeong²,

Lu³

2021

Preprint

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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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“…Here, we estimated 1/σ 2 using the method of moments. Alternatively, one can also use Hglm package in R (Rönnegård et al, 2010) to find the MLE of σ 2 or the argument of prior elicitation (Jeong, 2020).…”

Section: Calculation Of Credibility Premiums Under Various Parameter ...mentioning

confidence: 99%

On the ordering of credibility factors

Ahn¹,

Jeong²,

Lu³

2021

Preprint

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Traditional credibility analysis of risks in insurance is based on the random effects model, where the heterogeneity across the policyholders is assumed to be time-invariant. One popular extension is the dynamic random effects (or state-space) model. However, while the latter allows for time-varying heterogeneity, its application to the credibility analysis should be conducted with care due to the possibility of negative credibilities per period [see Pinquet (2020a)]. Another important but underexplored topic is the ordering of the credibility factors in a monotonous manner-recent claims ought to have larger weights than the old ones. This paper shows that the ordering of the covariance structure of the random effects in the dynamic random effects model does not necessarily imply that of the credibility factors. Subsequently, we show that the state-space model, with AR(1)-type autocorrelation function, guarantees the ordering of the credibility factors. Simulation experiments and a case study with a real dataset are conducted to show the relevance in insurance applications.

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Testing for Random Effects in Compound Risk Models via Bregman Divergence

Cited by 14 publications

References 30 publications

Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach

Approximation of Zero-Inflated Poisson Credibility Premium via Variational Bayes Approach

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

On the ordering of credibility factors

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