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Stochastic loss reserving: A new perspective from a Dirichlet model

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  • Karthik Sriram
  • Peng Shi

Abstract

Forecasting the outstanding claim liabilities to set adequate reserves is critical for a nonlife insurer's solvency. Chain–Ladder and Bornhuetter–Ferguson are two prominent actuarial approaches used for this task. The selection between the two approaches is often ad hoc due to different underlying assumptions. We introduce a Dirichlet model that provides a common statistical framework for the two approaches, with some appealing properties. Depending on the type of information available, the model inference naturally leads to either Chain–Ladder or Bornhuetter–Ferguson prediction. Using claims data on Worker's compensation insurance from several U.S. insurers, we discuss both frequentist and Bayesian inference.

Suggested Citation

  • Karthik Sriram & Peng Shi, 2021. "Stochastic loss reserving: A new perspective from a Dirichlet model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(1), pages 195-230, March.
    • Handle: RePEc:bla:jrinsu:v:88:y:2021:i:1:p:195-230
    DOI: 10.1111/jori.12311
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    References listed on IDEAS

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    1. Saluz, Annina & Gisler, Alois & Wüthrich, Mario V., 2011. "Development Pattern and Prediction Error for the Stochastic Bornhuetter-Ferguson Claims Reserving Method," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 279-313, November.
    2. Peters, Gareth W. & Wüthrich, Mario V. & Shevchenko, Pavel V., 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 36-51, August.
    3. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    4. Gareth W. Peters & Mario V. Wuthrich & Pavel V. Shevchenko, 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Papers 1004.2548, arXiv.org.
    5. 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.
    6. England, Peter & Verrall, Richard, 1999. "Analytic and bootstrap estimates of prediction errors in claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 281-293, December.
    7. Peng Shi, 2017. "A Multivariate Analysis of Intercompany Loss Triangles," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 717-737, June.
    8. 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.
    9. Alai, D. H. & Merz, M. & Wüthrich, M. V., 2009. "Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method," Annals of Actuarial Science, Cambridge University Press, vol. 4(1), pages 7-31, March.
    10. Mack, Thomas, 2008. "Correction Note to “The Prediction Error of Bornhuetter/Ferguson” By T. Mack," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 669-669, November.
    11. Mack, Thomas, 2008. "The Prediction Error of Bornhuetter/Ferguson," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 87-103, May.
    12. England, P. D. & Verrall, R. J., 2006. "Predictive Distributions of Outstanding Liabilities in General Insurance," Annals of Actuarial Science, Cambridge University Press, vol. 1(2), pages 221-270, September.
    13. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    14. Alai, D. H. & Merz, M. & Wüthrich, M. V., 2011. "Prediction Uncertainty in the Bornhuetter-Ferguson Claims Reserving Method: Revisited," Annals of Actuarial Science, Cambridge University Press, vol. 5(1), pages 7-17, March.
    15. Peng Shi & Brian M. Hartman, 2016. "Credibility in Loss Reserving," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(2), pages 114-132, April.
    16. Paulo J. R. Pinheiro & João Manuel Andrade e Silva & Maria De Lourdes Centeno, 2003. "Bootstrap Methodology in Claim Reserving," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 701-714, December.
    17. Shi, Peng, 2014. "A Copula Regression For Modeling Multivariate Loss Triangles And Quantifying Reserving Variability," ASTIN Bulletin, Cambridge University Press, vol. 44(1), pages 85-102, January.
    18. R. J. Verrall, 2004. "A Bayesian Generalized Linear Model for the Bornhuetter-Ferguson Method of Claims Reserving," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(3), pages 67-89.
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