IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v99y2021icp1-8.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668721000391
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2021.03.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    2. Roger Koenker, 2017. "Quantile Regression: 40 Years On," Annual Review of Economics, Annual Reviews, vol. 9(1), pages 155-176, September.
    3. 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.
    4. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers CWP36/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. 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.
    6. 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.
    7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    8. Steven Kou & Xianhua Peng, 2016. "On the Measurement of Economic Tail Risk," Operations Research, INFORMS, vol. 64(5), pages 1056-1072, October.
    9. 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.
    10. Wang, Ruodu & Ziegel, Johanna F., 2015. "Elicitable distortion risk measures: A concise proof," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 172-175.
    11. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    12. Saralees Nadarajah & Bo Zhang & Stephen Chan, 2014. "Estimation methods for expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 271-291, February.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Anthony Coache & Sebastian Jaimungal & 'Alvaro Cartea, 2022. "Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning," Papers 2206.14666, arXiv.org, revised May 2023.
    2. 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.
    3. 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.
    4. Timo Dimitriadis & Yannick Hoga, 2023. "Regressions under Adverse Conditions," Papers 2311.13327, arXiv.org, revised Jul 2024.
    5. Tobias Fissler & Michael Merz & Mario V. Wuthrich, 2021. "Deep Quantile and Deep Composite Model Regression," Papers 2112.03075, arXiv.org.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Rita Pimentel & Morten Risstad & Sjur Westgaard, 2022. "Predicting interest rate distributions using PCA & quantile regression," Digital Finance, Springer, vol. 4(4), pages 291-311, December.
    3. David Happersberger & Harald Lohre & Ingmar Nolte, 2020. "Estimating portfolio risk for tail risk protection strategies," European Financial Management, European Financial Management Association, vol. 26(4), pages 1107-1146, September.
    4. Yingying Jiang & Fuming Lin & Yong Zhou, 2021. "The kth power expectile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 83-113, February.
    5. Sánchez Serrano, Antonio, 2021. "The impact of non-performing loans on bank lending in Europe: An empirical analysis," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    6. Vidal-Llana, Xenxo & Guillén, Montserrat, 2022. "Cross-sectional quantile regression for estimating conditional VaR of returns during periods of high volatility," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    7. Qifa Xu & Lu Chen & Cuixia Jiang & Yezheng Liu, 2022. "Forecasting expected shortfall and value at risk with a joint elicitable mixed data sampling model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(3), pages 407-421, April.
    8. Dimitriadis, Timo & Schnaitmann, Julie, 2021. "Forecast encompassing tests for the expected shortfall," International Journal of Forecasting, Elsevier, vol. 37(2), pages 604-621.
    9. Ahmed, Walid M.A., 2021. "Stock market reactions to upside and downside volatility of Bitcoin: A quantile analysis," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    10. Timo Dimitriadis & Xiaochun Liu & Julie Schnaitmann, 2020. "Encompassing Tests for Value at Risk and Expected Shortfall Multi-Step Forecasts based on Inference on the Boundary," Papers 2009.07341, arXiv.org.
    11. Anne M. Lausier & Shaleen Jain, 2018. "Diversity in global patterns of observed precipitation variability and change on river basin scales," Climatic Change, Springer, vol. 149(2), pages 261-275, July.
    12. Chen, Zhao & Cheng, Vivian Xinyi & Liu, Xu, 2024. "Reprint: Hypothesis testing on high dimensional quantile regression," Journal of Econometrics, Elsevier, vol. 239(2).
    13. Chong-Chuo Chang & Oshamah Lin Lin & Oshamah Yu-Cheng Chang & Oshamah Kun-Zhan Hsu, 2023. "Impact of Financial Liberalization on Firm Risk," Advances in Decision Sciences, Asia University, Taiwan, vol. 27(3), pages 14-45, September.
    14. Ruodu Wang & Yunran Wei, 2020. "Risk functionals with convex level sets," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1337-1367, October.
    15. Damian Clarke & Manuel Llorca Jaña & Daniel Pailañir, 2023. "The use of quantile methods in economic history," Historical Methods: A Journal of Quantitative and Interdisciplinary History, Taylor & Francis Journals, vol. 56(2), pages 115-132, April.
    16. Sulkhan Chavleishvili & Simone Manganelli, 2024. "Forecasting and stress testing with quantile vector autoregression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 66-85, January.
    17. Sander Barendse, 2017. "Interquantile Expectation Regression," Tinbergen Institute Discussion Papers 17-034/III, Tinbergen Institute.
    18. Chen, Le-Yu & Lee, Sokbae, 2023. "Sparse quantile regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 2195-2217.
    19. Rui Evangelista & João Andrade E Silva & Esmeralda A. Ramalho, 2021. "How heterogeneous is the impact of energy efficiency on dwelling prices? Evidence from the application of the unconditional quantile hedonic model to the Portuguese residential market," Working Papers REM 2021/0186, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    20. Sebastian Bayer & Timo Dimitriadis, 2018. "Regression Based Expected Shortfall Backtesting," Papers 1801.04112, arXiv.org, revised Sep 2019.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:99:y:2021:i:c:p:1-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.