An Expectation-Maximization Algorithm for the Exponential-Generalized Inverse Gaussian Regression Model with Varying Dispersion and Shape for Modelling the Aggregate Claim Amount

Tzougas, George; Jeong, Himchan

doi:10.3390/risks9010019

Cited by 8 publications

(4 citation statements)

References 37 publications

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“…In their work, the authors introduced the LAAD penalty, and have studied its properties as a method to reduce the bias inherent in the regular Lasso method. Tzougas and Karlis [10] and Tzougas and Jeong [11] considered a regression framework using mixed exponential distributions with varying dispersion, and solved the problem using the EM algorithm.…”

Section: Overviewmentioning

confidence: 99%

Loss amount prediction from textual data using a double GLM with shrinkage and selection

et al. 2021

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The Gamma model has been widely utilized in a variety of fields, including actuarial science, where it has important applications in insurance loss predictions. Meanwhile, high dimensional models and their applications have become more common in the statistics literature in recent years. The availability of such high dimensional models have allowed the analysis of non-traditional data, including those containing textual descriptions of the response. In the models used in such applications, the dispersion may be designed to be related to a set of covariates, as opposed to being a single fixed value for the entire population. Following this approach, we incorporate a group Lasso type penalty in both the dispersion and the mean parameterization for a Gamma model, and illustrate its use in a predictive analytics application in actuarial science. In particular, we apply the method to an insurance claim prediction problem involving textual data analysis methods. Simulations are conducted to illustrate the variable selection and model fitting performance of our method.

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Section: Overviewmentioning

confidence: 99%

Loss amount prediction from textual data using a double GLM with shrinkage and selection

et al. 2021

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“…Other examples of continuous mixture distributions were studied by Fung and Seneta (2007) and Gómez-Déniz et al (2013). Also, some mixtures of continuous distributions have recently been considered in the actuarial literature in Tzougas and Karlis (2020) and Tzougas and Jeong (2021).…”

Section: Introductionmentioning

confidence: 99%

On the Use of Lehmann’s Alternative to Capture Extreme Losses in Actuarial Science

Gómez-Déniz,

Calderín-Ojeda

2023

Risks

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This paper studies properties and applications related to the mixture of the class of distributions built by the Lehmann’s alternative (also referred to in the statistical literature as max-stable or exponentiated distribution) of the form [G(·)]λ, where λ>0 and G(·) is a continuous cumulative distribution function. This mixture can be useful in economics, financial, and actuarial fields, where extreme and long tails appear in the empirical data. The special case in which G(·) is the Stoppa cumulative distribution function, which is a good description of the random behaviour of large losses, is studied in detail. We provide properties of this mixture, mainly related to the analysis of the tail of the distribution that makes it a candidate for fitting actuarial data with extreme observations. Inference procedures are discussed and applications to three well-known datasets are shown.

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“…Furthermore, several works have focused on understanding how the claim severity distribution is influenced by certain risk factors. See, for example, (Frees 2009;Laudagé et al 2019;Tzougas and Jeong 2021; Tzougas and Karlis 2020) among many more. However, even if the literature in the univariate setting is abundant, the bivariate, and/or multivariate, extensions of such models have not been explored in depth even if in non-life insurance, the actuary may often be concerned with modeling jointly different types of claims and their associated costs.…”

Section: Introductionmentioning

confidence: 99%

EM Estimation for the Bivariate Mixed Exponential Regression Model

Chen

Dassios

Tzougas

2022

Risks

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In this paper, we present a new family of bivariate mixed exponential regression models for taking into account the positive correlation between the cost of claims from motor third party liability bodily injury and property damage in a versatile manner. Furthermore, we demonstrate how maximum likelihood estimation of the model parameters can be achieved via a novel Expectation-Maximization algorithm. The implementation of two members of this family, namely the bivariate Pareto or, Exponential-Inverse Gamma, and bivariate Exponential-Inverse Gaussian regression models is illustrated by a real data application which involves fitting motor insurance data from a European motor insurance company.

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An Expectation-Maximization Algorithm for the Exponential-Generalized Inverse Gaussian Regression Model with Varying Dispersion and Shape for Modelling the Aggregate Claim Amount

Cited by 8 publications

References 37 publications

Loss amount prediction from textual data using a double GLM with shrinkage and selection

Loss amount prediction from textual data using a double GLM with shrinkage and selection

On the Use of Lehmann’s Alternative to Capture Extreme Losses in Actuarial Science

EM Estimation for the Bivariate Mixed Exponential Regression Model

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