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Insurance ratemaking using the Exponential-Lognormal regression model

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  • Tzougas, George
  • Yik, Woo Hee
  • Mustaqeem, Muhammad Waqar

Abstract

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.

Suggested Citation

  • Tzougas, George & Yik, Woo Hee & Mustaqeem, Muhammad Waqar, 2019. "Insurance ratemaking using the Exponential-Lognormal regression model," LSE Research Online Documents on Economics 101729, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:101729
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    File URL: http://eprints.lse.ac.uk/101729/
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    References listed on IDEAS

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    More about this item

    Keywords

    Exponential-Lognormal regression model; EM Algorithm; Motor Third Party Liability Insurance; ratemaking;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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