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Loss modeling with the size-biased lognormal mixture and the entropy regularized EM algorithm

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  • Bae, Taehan
  • Miljkovic, Tatjana

Abstract

The Erlang mixture with a common scale parameter is one of many popular models for modeling insurance losses. However, the actuarial literature recognizes and discusses some limitations of aforementioned model in approximate heavy-tailed distributions. In this paper, a size-biased left-truncated Lognormal (SB-ltLN) mixture is proposed as a robust alternative to the Erlang mixture for modeling left-truncated insurance losses with a heavy tail. The weak denseness property of the weighted Lognormal mixture is studied along with the tail behavior. Explicit analytical solutions are derived for moments and Tail Value at Risk based on the proposed model. An extension of the regularized expectation–maximization (REM) algorithm with Shannon's entropy weights (ewREM) is introduced for parameter estimation and variability assessment. The Operational Riskdata eXchange's left-truncated internal fraud loss data set is used to illustrate applications of the proposed model. Finally, the results of a simulation study show promising performance of the proposed SB-ltLN mixture in different simulation settings.

Suggested Citation

  • Bae, Taehan & Miljkovic, Tatjana, 2024. "Loss modeling with the size-biased lognormal mixture and the entropy regularized EM algorithm," Insurance: Mathematics and Economics, Elsevier, vol. 117(C), pages 182-195.
    • Handle: RePEc:eee:insuma:v:117:y:2024:i:c:p:182-195
    DOI: 10.1016/j.insmatheco.2024.05.003
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    References listed on IDEAS

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    More about this item

    Keywords

    Regularized EM algorithm; Shannon entropy; Size-biased mixture; Lognormal distribution; Left-truncated insurance losses;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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