IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v240y2024i1s0304407624000228.html
   My bibliography  Save this article

Enhanced pricing and management of bundled insurance risks with dependence-aware prediction using pair copula construction

Author

Listed:
  • Shi, Peng
  • Zhao, Zifeng

Abstract

We propose a dependence-aware predictive modeling framework for multivariate risks stemmed from an insurance contract with bundling features — an important type of policy increasingly offered by major insurance companies. The bundling feature naturally leads to longitudinal measurements of multiple insurance risks, and correct pricing and management of such risks is of fundamental interest to financial stability of the macroeconomy. We build a novel predictive model that fully captures the dependence among the multivariate repeated risk measurements. Specifically, the longitudinal measurement of each individual risk is first modeled using pair copula construction with a D-vine structure, and the multiple D-vines are then integrated by a flexible copula. While our analysis mainly focuses on multivariate insurance risks, the proposed model indeed contributes to the broad research area of longitudinal data analysis. In particular, it provides a unified modeling framework for multivariate longitudinal data that can accommodate different scales of measurements, including continuous, discrete, and mixed observations, and thus can be potentially useful for various economic studies. A computationally efficient sequential method is proposed for model estimation and inference, and its performance is investigated both theoretically and via simulation studies. In the application, we examine multivariate bundled risks in multi-peril property insurance using proprietary data from a commercial property insurance provider. The proposed model is found to provide improved decision making for several key insurance operations. For underwriting, we show that the experience rate priced by the proposed model leads to a 9% lift in the insurer’s net revenue. For reinsurance, we show that the insurer underestimates the risk of the retained insurance portfolio by 10% when ignoring the dependence among bundled insurance risks.

Suggested Citation

  • Shi, Peng & Zhao, Zifeng, 2024. "Enhanced pricing and management of bundled insurance risks with dependence-aware prediction using pair copula construction," Journal of Econometrics, Elsevier, vol. 240(1).
  • Handle: RePEc:eee:econom:v:240:y:2024:i:1:s0304407624000228
    DOI: 10.1016/j.jeconom.2024.105676
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407624000228
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jeconom.2024.105676?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. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    2. Dong Hwan Oh & Andrew J. Patton, 2017. "Modeling Dependence in High Dimensions With Factor Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 139-154, January.
    3. Frees, Edward W. & Young, Virginia R. & Luo, Yu, 1999. "A longitudinal data analysis interpretation of credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 229-247, May.
    4. Anastasios Panagiotelis & Claudia Czado & Harry Joe, 2012. "Pair Copula Constructions for Multivariate Discrete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1063-1072, September.
    5. Xiaohong Chen & Wei Biao Wu & Yanping Yi, 2009. "Efficient Estimation of Copula-based Semiparametric Markov Models," Cowles Foundation Discussion Papers 1691, Cowles Foundation for Research in Economics, Yale University, revised Mar 2009.
    6. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    7. Boucher, Jean-Philippe & Inoussa, Rofick, 2014. "A Posteriori Ratemaking With Panel Data," ASTIN Bulletin, Cambridge University Press, vol. 44(3), pages 587-612, September.
    8. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149, September.
    9. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    10. Peng Shi & Lu Yang, 2018. "Pair Copula Constructions for Insurance Experience Rating," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 122-133, January.
    11. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    12. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    13. Dong Hwan Oh & Andrew J. Patton, 2013. "Simulated Method of Moments Estimation for Copula-Based Multivariate Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 689-700, June.
    14. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    15. Barthel, Nicole & Geerdens, Candida & Killiches, Matthias & Janssen, Paul & Czado, Claudia, 2018. "Vine copula based likelihood estimation of dependence patterns in multivariate event time data," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 109-127.
    16. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    17. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
    18. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
    19. Stöber, Jakob & Hong, Hyokyoung Grace & Czado, Claudia & Ghosh, Pulak, 2015. "Comorbidity of chronic diseases in the elderly: Patterns identified by a copula design for mixed responses," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 28-39.
    20. Claudia Czado & Tilmann Gneiting & Leonhard Held, 2009. "Predictive Model Assessment for Count Data," Biometrics, The International Biometric Society, vol. 65(4), pages 1254-1261, December.
    21. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    22. Edward W. Frees, 2015. "Analytics of Insurance Markets," Annual Review of Financial Economics, Annual Reviews, vol. 7(1), pages 253-277, December.
    23. Gee Y. Lee, 2017. "General Insurance Deductible Ratemaking," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(4), pages 620-638, October.
    24. Bernard, Carole & Jiang, Xiao & Wang, Ruodu, 2014. "Risk aggregation with dependence uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 93-108.
    25. Ruodu Wang & Zuo Quan Xu & Xun Yu Zhou, 2019. "Dual utilities on risk aggregation under dependence uncertainty," Finance and Stochastics, Springer, vol. 23(4), pages 1025-1048, October.
    26. Chen, Xiaohong & Huang, Zhuo & Yi, Yanping, 2021. "Efficient estimation of multivariate semi-nonparametric GARCH filtered copula models," Journal of Econometrics, Elsevier, vol. 222(1), pages 484-501.
    27. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    28. Rosy Oh & Peng Shi & Jae Youn Ahn, 2020. "Bonus-Malus premiums under the dependent frequency-severity modeling," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(3), pages 172-195, March.
    29. Gao, Lisa & Shi, Peng, 2022. "Leveraging high-resolution weather information to predict hail damage claims: A spatial point process for replicated point patterns," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 161-179.
    Full references (including those not matched with items on IDEAS)

    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. Nagler, Thomas & Krüger, Daniel & Min, Aleksey, 2022. "Stationary vine copula models for multivariate time series," Journal of Econometrics, Elsevier, vol. 227(2), pages 305-324.
    2. Smith, Michael Stanley & Maneesoonthorn, Worapree, 2018. "Inversion copulas from nonlinear state space models with an application to inflation forecasting," International Journal of Forecasting, Elsevier, vol. 34(3), pages 389-407.
    3. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    4. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    5. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.
    6. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    7. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    8. Chen, Xiaohong & Xiao, Zhijie & Wang, Bo, 2022. "Copula-based time series with filtered nonstationarity," Journal of Econometrics, Elsevier, vol. 228(1), pages 127-155.
    9. Rubén Loaiza‐Maya & Michael S. Smith & Worapree Maneesoonthorn, 2018. "Time series copulas for heteroskedastic data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 332-354, April.
    10. Saeide Sefidi & Mojtaba Ganjali & Taban Baghfalaki, 2022. "Analysis of ordinal and continuous longitudinal responses using pair copula construction," METRON, Springer;Sapienza Università di Roma, vol. 80(2), pages 255-280, August.
    11. Brendan K. Beare & Juwon Seo, 2015. "Vine Copula Specifications for Stationary Multivariate Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 228-246, March.
    12. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Estimating non-linear serial and cross-interdependence between financial assets," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 837-846.
    13. Xiaohong Chen & Zhijie Xiao & Bo Wang, 2020. "Copula-Based Time Series With Filtered Nonstationarity," Cowles Foundation Discussion Papers 2242R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2020.
    14. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    15. Bladt, Martin & McNeil, Alexander J., 2022. "Time series copula models using d-vines and v-transforms," Econometrics and Statistics, Elsevier, vol. 24(C), pages 27-48.
    16. Bladt Martin & McNeil Alexander J., 2022. "Time series with infinite-order partial copula dependence," Dependence Modeling, De Gruyter, vol. 10(1), pages 87-107, January.
    17. Rémillard, Bruno & Papageorgiou, Nicolas & Soustra, Frédéric, 2012. "Copula-based semiparametric models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 30-42.
    18. Oleg Sokolinskiy & Dick van Dijk, 2011. "Forecasting Volatility with Copula-Based Time Series Models," Tinbergen Institute Discussion Papers 11-125/4, Tinbergen Institute.
    19. Zängerle, Daniel & Schiereck, Dirk, 2022. "Modelling and predicting enterprise‑level cyber risks in the context of sparse data availability," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 136276, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    20. Aristidis K. Nikoloulopoulos & Peter G. Moffatt, 2019. "Coupling Couples With Copulas: Analysis Of Assortative Matching On Risk Attitude," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 654-666, January.

    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:econom:v:240:y:2024:i:1:s0304407624000228. 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/jeconom .

    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.