Backtesting the Bayesian Bornhuetter-Ferguson method against traditional approaches in claims reserving

References

• Alai, D. H., Merz, M., and Wüthrich, M. V. (2011). Prediction uncer-tainty in the Bornhuetter-Ferguson claims reserving method: revisited. Annals of Actuarial Science, 5(1): 717. doi: 10.1017/S1748499510000023
   Google Scholar
• Bornhuetter, R. L. and Ferguson, R. E. (1972). The actuary and IBNR. In Proceedings of the casualty actuarial society, volume 59, pages 181-195.
   Google Scholar
• Efron, B. (1979). Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 7(1): 1-26. doi: 10.1214/aos/1176344552
   Web of Science ®Google Scholar
• Efron, B. and Tibshirani, R. J. (1993). An introduction to the bootstrap. Chapman and Hall.
   Google Scholar
• EIOPA (2015). Guidelines on the valuation of technical provisions. Technical report, EIOPA.
   Google Scholar
• England, P. (2002). Addendum to “Analytic and bootstrap estimates of prediction errors in claims reserving”. Insurance: Mathematics and Economics, 31(3): 461-466.
   Web of Science ®Google Scholar
• England, P. D. and Verrall, R. J. (2002). Stochastic claims reserving in general insurance. British Actuarial Journal, 8(3): 443-518. doi: 10.1017/S1357321700003809
   Google Scholar
• England, P. D., Verrall, R. J., and Wüthrich, M. V. (2012). Bayesian over-dispersed Poisson model and the Bornhuetter & Ferguson claims reserving method. Annals of Actuarial Science, 6(2): 258-283. doi: 10.1017/S1748499512000012
   Google Scholar
• Friedland, J. F. (2009). Estimating Unpaid Claims Using Basic Techniques. CAS.
   Google Scholar
• Gao, G. (2016). Three essays on Bayesian claims reserving methods in general insurance. PhD thesis, College of Business and Economics.
   Google Scholar
• Gilks, W. R., Best, N. G., and Tan, K. (1995). Adaptive rejection metropolis sampling within gibbs sampling. Journal of the Royal Statistical Society: Series C (Applied Statistics), 44(4): 455-472.
   Web of Science ®Google Scholar
• Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1): 97-109. doi: 10.1093/biomet/57.1.97
   Web of Science ®Google Scholar
• Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin: The Journal of the IAA, 23(2): 213-225. doi: 10.2143/AST.23.2.2005092
   Google Scholar
• Mack, T. (2006). Parameter Estimation for Bornhuetter/Ferguson. Casualty Actuarial Society Forum, pages 141-157.
   Google Scholar
• Mack, T. (2008). The prediction error of Bornhuetter/Ferguson. ASTIN Bulletin: The Journal of the IAA, 38(1): 87-103. doi: 10.1017/S0515036100015075
   Web of Science ®Google Scholar
• Martinek, L. (2019). Analysis of stochastic reserving models by means of NAIC claims data. Risks, 7(2): 62. doi: 10.3390/risks7020062
   Web of Science ®Google Scholar
• Martinek, L., Arato, M., and Malyusz, M. (2015). Comparison of stochastic claims reserving models in insurance. Available on ArXiv.
   Google Scholar
• Martínez-Miranda, M., Nielsen, J., and Verrall, R. (2013). Double chain ladder and bornhuetter-ferguson. North American Actuarial Journal, 17 : 101-113. doi: 10.1080/10920277.2013.793158
   Google Scholar
• Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. The journal of chemical physics, 21(6): 1087-1092. doi: 10.1063/1.1699114
   Web of Science ®Google Scholar
• Meyers, G. (2015). Stochastic loss reserving using Bayesian MCMC models. Casualty Actuarial Society.
   Google Scholar
• Meyers, G. and Shi, P. (2011a). Loss Reserving Data Pulled From NAIC Schedule P. Available at http://www.casact.org/research/in-dex.cfm.
   Google Scholar
• Meyers, G. G. and Shi, P. (2011b). The retrospective testing of stochastic loss reserve models. In Casualty Actuarial Society E-Forum, Summer.
   Google Scholar
• NAIC (2004). Market Share Reports for property/casualty groups and companies.Technical report, National Association of Insurance Commissioners. https://www.naic.org/prod_serv/MSR-PB-05.pdf.
   Google Scholar
• NAIC (2020). Uniform property & casualty product coding matrix. Technical report, National Association of Insurance Commissioners. https://www.naic.org/documents/industry_pcm_p_c_2020.pdf.
   Google Scholar
• Pinheiro, P. J., Andrade e Silva, J. M., and de Lourdes Centeno, M. (2003). Bootstrap methodology in claim reserving. Journal of Risk and Insurance, 70(4): 701-714. doi: 10.1046/j.0022-4367.2003.00071.x
   Web of Science ®Google Scholar
• Renshaw, A. and Verrall, R. (1998). A stochastic model underlying the chain-ladder technique. British Actuarial Journal, 4(04): 903-923. doi: 10.1017/S1357321700000222
   Google Scholar
• Shapland, M. R. (2016). Using the ODP Bootstrap Model: A Practitioner’s Guide. Casualty Actuarial Society.
   Google Scholar
• Shi, P., Basu, S., and Meyers, G. G. (2012). A bayesian log-normal model for multivariate loss reserving. North American Actuarial Journal, 16: 29-51. doi: 10.1080/10920277.2012.10590631
   Google Scholar
• Shi, P. and Frees, E. W. (2011). Dependent loss reserving using copulas. ASTIN Bulletin, 41: 449-486.
   Web of Science ®Google Scholar
• Tee, L. and Käärik, M. and Vii, R. (2017). On comparison of stochastic reserving methods with bootstrapping. Risks, 5(2): 1-21.
   Google Scholar
• Wang, S. and Chen, H. (2012). Back-Testing the ODP Bootstrap of the Paid Chain-Ladder Model with Actual Historical Claims Data. Variance, 8(2): 182-203.
   Google Scholar
• Wüthrich, M. V. (2017). Non-life insurance: mathematics & statistics. Available at SSRN.
   Google Scholar
• Wüthrich, M. V. and Merz, M. (2008). Stochastic claims reserving methods in insurance, volume 435. John Wiley & Sons.
   Google Scholar
• Wüthrich, M. V. and Merz, M. (2015). Stochastic claims reserving manual: Advances in dynamic modeling. Technical Report 15-34, Swiss Finance Institute Research Paper.
   Google Scholar
• Wüthrich, M. V. (2010). Accounting year effects modeling in the stochastic chain ladder reserving method. North American Actuarial Journal, 14(23) : 5-55.
   Google Scholar