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Insurance ratemaking using the Exponential-Lognormal regression model

Tzougas, George, Yik, Woo Hee and Mustaqeem, Muhammad Waqar (2019) Insurance ratemaking using the Exponential-Lognormal regression model. Annals of Actuarial Science. 1 - 30. ISSN 1748-4995

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Identification Number: 10.1017/S1748499519000034


This paper is concerned with presenting the Exponential-Lognormal (ELN) regression model as a competitive alternative to the Pareto, or Exponential-Inverse Gamma, regression model that has been used in a wide range of areas, including insurance ratemaking. This is the first time that the ELN regression model is used in a statistical or actuarial context. The main contribution of the study is that we illustrate how maximum likelihood estimation of the ELN regression model, which does not have a density in closed form, can be accomplished relatively easily via an Expectation-Maximisation type algorithm. A real data application based on motor insurance data is examined in order to emphasise the versatility of the proposed algorithm. Finally, assuming that the number of claims is distributed according to the classic Negative Binomial and Poisson-Inverse Gaussian regression models, both the a priori and a posteriori, or Bonus–Malus, premium rates resulting from the ELN regression model are calculated via the net premium principle and compared to those determined by the Pareto regression model that has been traditionally used for modelling claim sizes.

Item Type: Article
Official URL:
Additional Information: © 2019 Institute and Faculty of Actuaries
Divisions: Statistics
Subjects: Q Science > QA Mathematics
H Social Sciences > HG Finance
Date Deposited: 26 Sep 2019 10:30
Last Modified: 16 May 2024 02:50

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