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Estimating loss reserves using hierarchical Bayesian Gaussian process regression with input warping

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  • Lally, Nathan
  • Hartman, Brian

Abstract

In this paper, we visualize the loss reserve runoff triangle as a spatially-organized data set. We apply Gaussian Process (GP) regression with input warping and several covariance functions to estimate future claims. We then compare our results over a range of product lines, including workers’ comp, medical malpractice, and personal auto. Even though the claims development of the lines are very different, the GP method is very flexible and can be applied to each without much customization. We find that our model generally outperforms the classical chain ladder model as well as the recently proposed hierarchical growth curve models of Guszcza (2008) in terms of point-wise predictive accuracy and produces dramatically better estimates of outstanding claims liabilities.

Suggested Citation

  • Lally, Nathan & Hartman, Brian, 2018. "Estimating loss reserves using hierarchical Bayesian Gaussian process regression with input warping," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 124-140.
    • Handle: RePEc:eee:insuma:v:82:y:2018:i:c:p:124-140
    DOI: 10.1016/j.insmatheco.2018.06.008
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    References listed on IDEAS

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    1. Peters, Gareth W. & Shevchenko, Pavel V. & Wüthrich, Mario V., 2009. "Model Uncertainty in Claims Reserving within Tweedie's Compound Poisson Models," ASTIN Bulletin, Cambridge University Press, vol. 39(1), pages 1-33, May.
    2. Katrien Antonio & Jan Beirlant, 2008. "Issues in Claims Reserving and Credibility: A Semiparametric Approach With Mixed Models," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 643-676, September.
    3. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    4. Yanwei Zhang & Vanja Dukic & James Guszcza, 2012. "A Bayesian non‐linear model for forecasting insurance loss payments," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 175(2), pages 637-656, April.
    5. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Model uncertainty in claims reserving within Tweedie's compound Poisson models," Papers 0904.1483, arXiv.org.
    6. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.
    7. de Alba, Enrique & Nieto-Barajas, Luis E., 2008. "Claims reserving: A correlated Bayesian model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 368-376, December.
    8. Peng Shi & Brian M. Hartman, 2016. "Credibility in Loss Reserving," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(2), pages 114-132, April.
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    Cited by:

    1. Anas Abdallah & Lan Wang, 2023. "Rank-Based Multivariate Sarmanov for Modeling Dependence between Loss Reserves," Risks, MDPI, vol. 11(11), pages 1-37, October.

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