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Deep quantile and deep composite triplet regression

Author

Listed:
  • Fissler, Tobias
  • Merz, Michael
  • Wüthrich, Mario V.

Abstract

A main difficulty in actuarial claim size modeling is that covariates may have different effects on the body of the conditional distribution and on its tail. To cope with this problem, we introduce a deep composite regression model whose splicing point is given in terms of a quantile of the conditional claim size distribution (rather than a constant). This allows us to simultaneously fit different regression models in the two different parts of the conditional distribution function. To facilitate M-estimation for such models, we introduce and characterize the class of strictly consistent scoring functions for the triplet consisting of a quantile, as well as the lower and upper expected shortfall beyond that quantile. In a second step, this elicitability result is applied to fit deep neural network regression models. We demonstrate the applicability of our approach and its superiority over classical approaches on a real data set from accident insurance.

Suggested Citation

  • Fissler, Tobias & Merz, Michael & Wüthrich, Mario V., 2023. "Deep quantile and deep composite triplet regression," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 94-112.
    • Handle: RePEc:eee:insuma:v:109:y:2023:i:c:p:94-112
    DOI: 10.1016/j.insmatheco.2023.01.001
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    References listed on IDEAS

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    More about this item

    Keywords

    Elicitability; Consistent loss function; Proper scoring rule; Bregman divergence; Quantile and expected shortfall regression; Conditional tail expectation; Neural network regression; Splicing model;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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