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Bayesian Claims Reserving Methods in Non-life Insurance with Stan

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Abstract

This chapter briefly reviews Bayesian statistics, Markov chain Monte Carlo methods, and non-life insurance claims reserving methods. Some of the most influential literature are listed in this chapter. Two Bayesian inferential engines, BUGS and Stan, are introduced. At the end the monograph structure is given and the general notation is introduced.

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References

  • Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society, 330–418.

    Google Scholar 

  • Bornhuetter, R. L., & Ferguson, R. E. (1972). The actuary and IBNR. Proceedings of the Casualty Actuarial Society, 59, 181–195.

    Google Scholar 

  • Box, G. E., & Tiao, G. C. (1973). Bayesian inference in statistical analysis. New York: Wiley Classics.

    MATH  Google Scholar 

  • Brehm, P. J., Gluck, S., Kreps, R., Major, J., Mango, D., & Shaw, R., et al. (2007). Enterprise risk analysis for property and liability insurance companies: A practical guide to standard models and emerging solutions. New York: Guy Carpenter & Company.

    Google Scholar 

  • Bühlmann, H. (1967). Experience rating and credibility. ASTIN Bulletin, 4, 199–207.

    Article  Google Scholar 

  • Christiansen, M. C., & Niemeyer, A. (2014). The fundamental definition of the solvency capital requirement in Solvency II. ASTIN Bulletin, 44, 501–533.

    Article  MathSciNet  Google Scholar 

  • Duane, S., Kennedy, A. D., Pendleton, B. J., & Roweth, D. (1987). Hybrid Monte Carlo. Physics Letters B, 195, 216–222.

    Article  Google Scholar 

  • England, P. D., & Verrall, R. J. (2002). Stochastic claims reserving in general insurance. British Actuarial Journal, 8, 443–518.

    Article  Google Scholar 

  • England, P. D., Verrall, R. J., & Wüthrich, M. V. (2012). Bayesian over-dispersed poisson model and the Bornhuetter-Ferguson claims reserving method. Annals of Actuarial Science, 6, 258–283.

    Article  Google Scholar 

  • Gelfand, A. E., & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.

    Article  MathSciNet  Google Scholar 

  • Gelfand, A. E., Hills, S. E., Racinepoon, A., & Smith, A. F. M. (1990). Illustration of Bayesian-inference in normal data models using Gibbs sampling. Journal of the American Statistical Association, 85, 972–985.

    Article  Google Scholar 

  • Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2014). Bayesian data analysis (3rd ed.). Boca Raton: Chapman & Hall.

    MATH  Google Scholar 

  • Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.

    Article  Google Scholar 

  • Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika, 82, 711–732.

    Article  MathSciNet  Google Scholar 

  • Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: Data mining, inference, and prediction (2nd ed.). Springer, New York.

    Google Scholar 

  • Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97–109.

    Article  MathSciNet  Google Scholar 

  • Jeffreys, H. (1961). Theory of probability (3rd ed.). London: Oxford University Press.

    MATH  Google Scholar 

  • Joe, H., & Xu, J. J. (1996). The estimation method of inference functions for margins for multivariate models. http://hdl.handle.net/2429/57078.

  • Joe, H. (2014). Dependence modeling with copulas. New York: Chapman & Hall.

    Book  Google Scholar 

  • Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999). An introduction to variational methods for graphical models. Machine Learning, 37, 183–233.

    Article  Google Scholar 

  • Laplace, P. S. (1785). Memoire sur les approximations des formules qui sont fonctions de tres grands nombres. In Memoires de l’Academie Royale des Sciences.

    Google Scholar 

  • Laplace, P. S. (1810). Memoire sur les approximations des formules qui sont fonctions de tres grands nombres, et sur leur application aux probabilites. In Memoires de l’Academie des Science de Paris.

    Google Scholar 

  • Lindley, D. V. (1965). Introduction to probability and statistics from Bayesian viewpoint (Vol. 2). Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Longley-Cook, L. H. (1962). An introduction to credibility theory. Proceedings of the Casualty Actuarial Society, 49, 194–221.

    Google Scholar 

  • Lunn, D., Jackson, C., Best, N., Thomas, A., & Spiegelhalter, D. (2012). The BUGS book: A practical introduction to Bayesian analysis. Boca Raton: Chapman & Hall.

    Google Scholar 

  • Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23, 213–225.

    Article  Google Scholar 

  • Mack, T. (1999). The standard error of chain-ladder reserve estimates, recursive calculation and inclusion of a tail factor. ASTIN Bulletin, 29, 361–366.

    Article  Google Scholar 

  • Mack, T. (2008). The prediction error of Bornhuetter-Ferguson. ASTIN Bulletin, 38, 87.

    Article  MathSciNet  Google Scholar 

  • Mayerson, A. L. (1964). A Bayesian view of credibility. Proceedings of the Casualty Actuarial Society, 51, 7–23.

    Google Scholar 

  • Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.

    Article  Google Scholar 

  • Neal, R. M. (1994). An improved acceptance procedure for the hybrid Monte Carlo algorithm. Journal of Computational Physics, 111, 194–203.

    Article  MathSciNet  Google Scholar 

  • Simpson, L., & McCourt, P. (2012). Worksafe Victoria actuarial valuation of outstanding claims liability for the scheme as at 30 June 2012, Technical report. PricewaterhouseCoopers Actuarial Pty Ltd.

    Google Scholar 

  • Taylor, G. (2000). Loss reserving: An actuarial perspective. Boston: Kluwer Academic Publishers.

    Google Scholar 

  • Whitney, A. W. (1918). The theory of experience rating. Proceedings of the Casualty Actuarial Society, 4, 274–292.

    Google Scholar 

  • Wüthrich, M. V., & Merz, M. (2008). Stochastic claims reserving methods in insurance. Chichester: Wiley & Sons.

    MATH  Google Scholar 

  • Wüthrich, M. V., & Merz, M. (2015). Stochastic claims reserving manual: Advances in dynamic modelling. SSRN, ID 2649057.

    Google Scholar 

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Authors and Affiliations

  1. School of Statistics, Renmin University of China, Beijing, China

    Guangyuan Gao

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  1. Guangyuan Gao
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Correspondence to Guangyuan Gao .

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Gao, G. (2018). Introduction. In: Bayesian Claims Reserving Methods in Non-life Insurance with Stan. Springer, Singapore. https://doi.org/10.1007/978-981-13-3609-6_1

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