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

Tzougas, George; Makariou, Despoina

doi:10.1111/rmir.12224

Cited by 3 publications

(2 citation statements)

References 60 publications

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“…Note that one can use different distributions instead of gamma distribution to describe the behavior of random θ ji as long as E[θ ji ] = 1 for an identifiability issue. For more details on the use of distributions for random θ ji other than gamma when N jit |θ ji follows a Poisson distribution, please see Tzougas (2020) and Tzougas and Makariou (2022).…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

Nonparametric intercept regularization for insurance claim frequency regression models

Lee,

Jeong

2024

Ann. actuar. sci.

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“…In our case, we assume that such a parameter is unknown and show that it can be efficiently estimated. Also, a multivariate PGIG model under a regression framework has been proposed by Tzougas and Makariou (2022), but this model cannot handle time series data.…”

Section: Introductionmentioning

confidence: 99%

A multivariate heavy-tailed integer-valued GARCH process with EM algorithm-based inference

Jang,

Sundararajan,

Barreto-Souza

2023

Stat Comput

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A new multivariate integer-valued Generalized AutoRegressive Conditional Heteroscedastic (GARCH) process based on a multivariate Poisson generalized inverse Gaussian distribution is proposed. The estimation of parameters of the proposed multivariate heavy-tailed count time series model via maximum likelihood method is challenging since the likelihood function involves a Bessel function that depends on the multivariate counts and its dimension. As a consequence, numerical instability is often experienced in optimization procedures. To overcome this computational problem, two feasible variants of the expectation-maximization (EM) algorithm are proposed for estimating the parameters of our model under low and high-dimensional settings. These EM algorithm variants provide computational benefits and help avoid the difficult direct optimization of the likelihood function from the proposed process. Our model and proposed estimation procedures can handle multiple features such as modeling of multivariate counts, heavy-tailedness, overdispersion, accommodation of outliers, allowances for both positive and negative autocorrelations, estimation of cross/contemporaneous-correlation, and the efficient estimation of parameters from both statistical and computational points of view. Extensive Monte Carlo simulation studies are presented to assess the performance of the proposed EM algorithms. Two empirical applications of our approach are provided. The first application concerns modeling bivariate count time series data on cannabis possession-related offenses in Australia, while the second one involves modeling intraday high-frequency financial transactions data from multiple holdings in the U.S. financial market.

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A Review of Generalized Hyperbolic Distributions

Jiang,

Nadarajah,

Hitchen

2023

Comput Econ

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

Cited by 3 publications

References 60 publications

Nonparametric intercept regularization for insurance claim frequency regression models

Nonparametric intercept regularization for insurance claim frequency regression models

A multivariate heavy-tailed integer-valued GARCH process with EM algorithm-based inference

A Review of Generalized Hyperbolic Distributions

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