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Joint generalized quantile and conditional tail expectation regression for insurance risk analysis

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  • Guillen, Montserrat
  • Bermúdez, Lluís
  • Pitarque, Albert

Abstract

Based on recent developments in joint regression models for quantile and expected shortfall, this paper seeks to develop models to analyse the risk in the right tail of the distribution of non-negative dependent random variables. We propose an algorithm to estimate conditional tail expectation regressions, introducing generalized risk regression models with link functions that are similar to those in generalized linear models. To preserve the natural ordering of risk measures conditional on a set of covariates, we add extra non-negative terms to the quantile regression. A case using telematics data in motor insurance illustrates the practical implementation of predictive risk models and their potential usefulness in actuarial analysis.

Suggested Citation

  • Guillen, Montserrat & Bermúdez, Lluís & Pitarque, Albert, 2021. "Joint generalized quantile and conditional tail expectation regression for insurance risk analysis," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 1-8.
    • Handle: RePEc:eee:insuma:v:99:y:2021:i:c:p:1-8
    DOI: 10.1016/j.insmatheco.2021.03.006
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    References listed on IDEAS

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    1. Ana M. Pérez-Marín & Montserrat Guillen & Manuela Alcañiz & Lluís Bermúdez, 2019. "Quantile Regression with Telematics Information to Assess the Risk of Driving above the Posted Speed Limit," Risks, MDPI, vol. 7(3), pages 1-11, July.
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    3. James W. Taylor, 2019. "Forecasting Value at Risk and Expected Shortfall Using a Semiparametric Approach Based on the Asymmetric Laplace Distribution," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 121-133, January.
    4. Jean-Philippe Boucher & Steven Côté & Montserrat Guillen, 2017. "Exposure as Duration and Distance in Telematics Motor Insurance Using Generalized Additive Models," Risks, MDPI, vol. 5(4), pages 1-23, September.
    5. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
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    10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    11. Mercedes Ayuso & Montserrat Guillen & Ana María Pérez-Marín, 2016. "Telematics and Gender Discrimination: Some Usage-Based Evidence on Whether Men’s Risk of Accidents Differs from Women’s," Risks, MDPI, vol. 4(2), pages 1-10, April.
    12. Wang, Ruodu & Ziegel, Johanna F., 2015. "Elicitable distortion risk measures: A concise proof," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 172-175.
    13. Montserrat Guillen & Jens Perch Nielsen & Mercedes Ayuso & Ana M. Pérez‐Marín, 2019. "The Use of Telematics Devices to Improve Automobile Insurance Rates," Risk Analysis, John Wiley & Sons, vol. 39(3), pages 662-672, March.
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    Cited by:

    1. Timo Dimitriadis & Yannick Hoga, 2023. "Regressions under Adverse Conditions," Papers 2311.13327, arXiv.org.
    2. Anthony Coache & Sebastian Jaimungal & 'Alvaro Cartea, 2022. "Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning," Papers 2206.14666, arXiv.org, revised May 2023.
    3. Xenxo Vidal-Llana & Carlos Salort Sánchez & Vincenzo Coia & Montserrat Guillen, 2022. ""Non-Crossing Dual Neural Network: Joint Value at Risk and Conditional Tail Expectation estimations with non-crossing conditions"," IREA Working Papers 202215, University of Barcelona, Research Institute of Applied Economics, revised Oct 2022.
    4. Tobias Fissler & Michael Merz & Mario V. Wuthrich, 2021. "Deep Quantile and Deep Composite Model Regression," Papers 2112.03075, arXiv.org.
    5. 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.
    6. Marcelo Brutti Righi & Fernanda Maria Muller & Marlon Ruoso Moresco, 2022. "A risk measurement approach from risk-averse stochastic optimization of score functions," Papers 2208.14809, arXiv.org, revised May 2023.

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