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Actuarial Modeling with MCMC and BUGs

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  • David Scollnik

Abstract

In this paper, the author reviews some aspects of Bayesian data analysis and discusses how a variety of actuarial models can be implemented and analyzed in accordance with the Bayesian paradigm using Markov chain Monte Carlo techniques via the BUGS (Bayesian inference Using Gibbs Sampling) suite of software packages. The emphasis is placed on actuarial loss models, but other applications are referenced, and directions are given for obtaining documentation for additional worked examples on the World Wide Web.

Suggested Citation

  • David Scollnik, 2001. "Actuarial Modeling with MCMC and BUGs," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 96-124.
    • Handle: RePEc:taf:uaajxx:v:5:y:2001:i:2:p:96-124
    DOI: 10.1080/10920277.2001.10595987
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    Cited by:

    1. Alessandro Ricotta & Edoardo Luini, 2019. "Bayesian Estimation of Structure Variables in the Collective Risk Model for Reserve Risk," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 9(2), pages 1-2.
    2. Verrall, R.J. & England, P.D., 2005. "Incorporating expert opinion into a stochastic model for the chain-ladder technique," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 355-370, October.
    3. Merz, Michael & Wüthrich, Mario V., 2010. "Paid-incurred chain claims reserving method," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 568-579, June.
    4. Simon CK Lee, 2020. "Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing," Risks, MDPI, vol. 8(1), pages 1-21, February.
    5. Alexandre Boumezoued & Yoboua Angoua & Laurent Devineau & Jean-Philippe Boisseau, 2011. "One-year reserve risk including a tail factor: closed formula and bootstrap approaches," Papers 1107.0164, arXiv.org, revised Apr 2012.
    6. .Fernández Huerga, E., 2004. "Causas de la utilización del empleo temporal y la subcontratación: Análisis empírico de las industrias extractivas en León," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 22, pages 371(30á)-37, Agosto.
    7. Migon, Helio S. & Moura, Fernando A.S., 2005. "Hierarchical Bayesian collective risk model: an application to health insurance," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 119-135, April.
    8. Bente Corneliu Cristian & Gavriletea Marius Dan, 2015. "Inflation Adjusted Chain Ladder Method," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(2), pages 370-379, December.
    9. Michelle Xia, 2018. "Bayesian Adjustment for Insurance Misrepresentation in Heavy-Tailed Loss Regression," Risks, MDPI, vol. 6(3), pages 1-16, August.
    10. Alexandre Boumezoued & Yoboua Angoua & Laurent Devineau & Jean-Philippe Boisseau, 2011. "One-year reserve risk including a tail factor: closed formula and bootstrap approaches," Working Papers hal-00605329, HAL.
    11. Kogure Atsuyuki & Kitsukawa Kenji & Kurachi Yoshiyuki, 2009. "A Bayesian Comparison of Models for Changing Mortalities toward Evaluating Longevity Risk in Japan," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(2), pages 1-22, April.
    12. Emilio Gomez-deniz & Francisco Vazquez-polo, 2005. "Modelling uncertainty in insurance Bonus-Malus premium principles by using a Bayesian robustness approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 771-784.
    13. Koissi, Marie-Claire & Shapiro, Arnold F., 2006. "Fuzzy formulation of the Lee-Carter model for mortality forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 287-309, December.
    14. Ozkok, Erengul & Streftaris, George & Waters, Howard R. & Wilkie, A. David, 2012. "Bayesian modelling of the time delay between diagnosis and settlement for Critical Illness Insurance using a Burr generalised-linear-type model," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 266-279.

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