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. We also explain how to generalize those copulas in the format of a vine copula. 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.
Bibliographical noteFunding Information:
This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [2016R1D1A1B03936100] and Next-Generation BioGreen 21 program, Rural Development Administration, Republic of Korea [PJ01337701] and National Research Foundation of Korea (NRF) grant funded by the Korean Government [2020R1F1A1A01061202].
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- Collective risk model
- Gaussian copula
- frequency-severity dependence
- vine copula