Recently, a body of literature proposed new models relaxing a widely-used but controversial assumption of independence between claim frequency and severity in non-life insurance rate making. This paper critically reviews a generalized linear model approach, where a dependence between claim frequency and severity is introduced by treating frequency as a covariate in a regression model for severity. As an extension of this approach, we propose a dispersion model for severity. For this model, the information loss caused by using average severity rather than individual severity is examined in detail and the parameter estimators suffering from low efficiency are identified. We also provide analytical solutions for the aggregate sum to help rate making. We show that the simple functional form used in current research may not properly reflect the real underlying dependence structure. A real data analysis is given to explain our analytical findings.
Bibliographical noteFunding Information:
Woojoo Lee was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2016R1D1A1B03936100 ). Sojung C. Park appreciates the support from the Institute of Management Research and Big Data Institute at Seoul National University . Jae Youn Ahn was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government ( NRF-2017R1D1A1B03032318 ).
© 2018 The Korean Statistical Society
- Dispersion parameter
- Generalized linear model
- Rate making