A Comparative Perspective on Multivariate Modeling of Insurance Compensation Payments with Regression-Based and Copula-Based Models

Year 2023, Issue: 39, 161 - 171, 27.12.2023

Övgücan Karadağ Erdemir

Abstract

In this study, compensation payments for Turkish motor vehicles’ compulsory third-party liability insurance between 2018 and 2022 are modeled from a comparative perspective using regression-based and copula-based multivariate statistical methods. The assumption of gamma distribution for logarithmic compensation payment variables is carried out in both approaches. Bivariate gamma regression is established using the bivariate gamma distribution, and the mixture of experts, one of the machine learning techniques, is employed to form the mixture of bivariate gamma regressions. The bivariate copula regression and finite mixture of copula regression models are designed using the Gumbel and Frank copula functions. The computational analyses were conducted using the mvClaim package in R. Based on the comparison of model results, a mixture of copula-based models is found to be more suitable for the multivariate modeling of insurance compensation payments.

Keywords

Bivariate Gamma Distribution, Copula, Generalized Linear Model, Copula Regression, Insurance Compensation Payments, Machine Learning Techniques, Mixture of Experts Model

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