Robust bootstrap procedures for the chain-ladder method

References

• Amado, C., Bianco, A. M., Boente, G. & Piers, A. M. (2014). Robust bootstrap: An alternative to bootstrapping robust estimators. REVSTAT -- Statistical Journal 12(2), 169–197.
   Web of Science ®Google Scholar
• Amado, C. & Pires, A. M. (2004). Robust bootstrap with non random weights based on the influence function. Communications in Statistics -- Simulation and Computation 33(2), 377–396.
   Web of Science ®Google Scholar
• Antonio, K. & Plat, R. (2014). Micro-level stochastic loss reserving for general insurance. Scandinavian Actuarial Journal 2014(7), 649–669.
   Web of Science ®Google Scholar
• Ashe, F. (1986). An essay at measuring the variance of estimates of outstanding claim payments. ASTIN Bulletin 16, S99–S113.
   Google Scholar
• Barnett, G. & Zehnwirth, B., (2008). Modeling with the multivariate probabilistic trend family. Casualty Actuarial Society E-forum 2008. Available at http://www.casact.org/pubs/forum/
   Google Scholar
• Boisseau, J.-P., (2006). Solvabilité 2 et mesure de volatilité dans les provisions pour sinistres à payer [Solvency II and volatility measures in claims reserves]. Mémoire Centre D’études Actuarielles.
   Google Scholar
• Boumezoued, A., Angoua, Y., Devineau, L., Boisseau, J.-P. (2012). One-year reserve risk including a tail factor: Closed formula and bootstrap approaches. arXiv, 1107.0164
   Google Scholar
• Brazauskas, V. (2009). Robust and efficient fitting of loss models: Diagnostic tools and insights. North American Actuarial Journal 13(3), 356–369.
   Google Scholar
• Brazauskas, V., Jones, B. L. & Zitikis, R. (2009). Robust fitting of claim severity distributions and the method of trimmed moments. Journal of Statistical Planning and Inference 139(6), 2028–2043.
   Web of Science ®Google Scholar
• Camponovo, L., Scaillet, O. & Trojani, F. (2012). Robust subsampling. Journal of Econometrics 167(1), 197–210.
   Web of Science ®Google Scholar
• Cantoni, E. & Ronchetti, E. (2001). Robust inference for generalized linear models. Journal of the American Statistical Association 96, 1022–1030.
   Web of Science ®Google Scholar
• Chatterjee, A. & Lahiri, S. N. (2011). Bootstrapping lasso estimators. Journal of the American Statistical Association 106(494), 608–625.
   Web of Science ®Google Scholar
• Cordeiro, G. M. (2004). On pearson’s residuals in generalized linear models. Statistics & Probability Letters 66(3), 213–219.
   Web of Science ®Google Scholar
• Cowell, R., Exploration of a novel bootstrap technique for estimating the distribution of outstanding claims reserves in general insurance, Working Paper Actuarial Research Paper No. 192 2009, City University London: London, UK.
   Google Scholar
• Dell’Aquila, R. & Embrechts, P. (2006). Extremes and robustness: A contradiction? Financial Markets and Portfolio Management 20, 103–118.
   Google Scholar
• Diers, D. (2009). Stochastic re-reserving in multi-year internal models. An approach based on simulations. ASTIN Colloquium. Helsinki. Available at http://www.actuaries.org/EVENTS/Congresses/Cape_Town/Papers/Non-Life%20Insurance%20(ASTIN)/53_final%20paper_Diers.pdf
   Google Scholar
• Dreksler, S., Allen, C., Akoh-Arrey, A., Courchene, J. A., Junaid, B., Kirk, J., Lowe, W., O’Dea, S., Piper, J., Shah, M., Shaw, G., Storman, D., Thaper, S., Thomas, L., Wheatley, M. & Wilson, M. (2015). Solvency II technical provisions for general insurers. British Actuarial Journal 20, 7–129.
   Web of Science ®Google Scholar
• Efron, B. (1981). Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods. Biometrika 68(3), 589–599.
   Web of Science ®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. & Verrall, R. (1999). Analytic and bootstrap estimates of prediction errors in claims reserving. Insurance: Mathematics and Economics 25(3), 281–293.
   Web of Science ®Google Scholar
• England, P. & Verrall, R. (2002). Stochastic claims reserving in general insurance. British Actuarial Journal 8, 443–518.
   Google Scholar
• England, P. D. & Verrall, R. J. (2006). Predictive distributions of outstanding liabilities in general insurance. Annals of Actuarial Science 1, 221–270.
   Google Scholar
• Hall, P., Horowitz, J. L. & Jing, B.-Y. (1995). On blocking rules for the bootstrap with dependent data. Biometrika 82(3), 561–574.
   Web of Science ®Google Scholar
• Hampel, F. (1974). The influence curve and its role in robust estimation. Journal of the American Statistical Association 69, 383–393.
   Web of Science ®Google Scholar
• Hampel, F., Ronchetti, E., Rousseeuw, P. & Stahel, W. (1986). Robust Statistics: The Approach Based on Influence Functions. New York: Wiley.
   Google Scholar
• Hoedemakers, T., Beirlant, J., Goovaerts, M. J. & Dhaene, J. (2005). On the distribution of discounted loss reserves using generalized linear models. Scandinavian Actuarial Journal 2005(1), 25–45.
   Google Scholar
• Hubert, M., Dierckx, G. & Vanpaemel, D. (2013). Detecting influential data points for the Hill estimator in Pareto-type distributions. Computational Statistics & Data Analysis 65, 13–28.
   Web of Science ®Google Scholar
• Johnson, N.L., Kotz, S. & Kemp, A.W., (1993). Univariate discrete distributions, 2nd ed., New York: Wiley.
   Google Scholar
• Kaas, R., Goovaerts, M., Dhaene, J. & Denuit, M. (2009). Modern actuarial risk theory: Using R. Berlin: Springer.
   Google Scholar
• Kremer, E. (1982). Ibnr-claims and the two-way model of anova. Scandinavian Actuarial Journal 1982(1), 47–55.
   Google Scholar
• Lacoume, A., (2008). Mesure du risque de réserve sur un horizon de un an [Risk measures in claims reserves over a one-year time horizon]. Mémoire ISFA. Institut De Science Financiere Et D’assurances, Université Claude Bernard -- Lyon 1, Villeurbanne.
   Google Scholar
• Lowe, J., (1994). A practical guide to measuring reserve variability using: Bootstrapping, operational time and a distribution free approach. Proceedings of the 1994 General Insurance Convention, Institue if Actuaries and Faculty if Actuaries, Glasgow.
   Google Scholar
• Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin 23, 213–225.
   Google Scholar
• Mack T., (1994). Measuring the variability of chain ladder reserve estimates. Casualty Actuarial Society Forum, 101–182.
   Google Scholar
• Mack, T., Quarg, G. & Braun, C. (2006). The mean square error of prediction in the chain ladder reserving method - a comment. ASTIN Bulletin 36, 543–552.
   Web of Science ®Google Scholar
• McCullagh, P. & Nelder, J. A. (1983). Generalized linear models. London: Chapman & Hall.
   Google Scholar
• Norberg, R. (1993). Prediction of outstanding liabilities in non-life insurance. Astin Bulletin 23(01), 95–115.
   Google Scholar
• Ohlsson, E. & Lauzeningks, J. (2009). The one-year non-life insurance risk. Insurance: Mathematics and Economics 45(2), 203–208.
   Web of Science ®Google Scholar
• Pinheiro, P. J. R., Andrade e Silva, J. M. & De Lourdes Centeno, M. (2003). Bootstrap methodology in claim reserving. Journal of Risk and Insurance 70(4), 701–714.
   Web of Science ®Google Scholar
• Pison, G. & Van Aelst, S. (2004). Diagnostic plots for robust multivariate methods. Journal of Computational and Graphical Statistics 13, 310–329.
   Web of Science ®Google Scholar
• Pitselis, G., Grigoriadou, V. & Badounas, I. (2015). Robust loss reserving in a log-linear model. Insurance: Mathematics and Economics 64, 14–27.
   Web of Science ®Google Scholar
• Renshaw, A. & Verrall, R. (1998). A stochastic model underlying the chain-ladder technique. British Actuarial Journal 4, 903–923.
   Google Scholar
• Salibian-Barrera, M., Van Aelst, S. & Willems, G. (2008). Fast and robust bootstrap. Statistical Methods and Applications 17(1), 41–71.
   Web of Science ®Google Scholar
• Salibian-Barrera, M., Zamar, R.H. (2002). Bootstrapping robust estimates of regression. The Annals of Statistics 30(2), 556–582.
   Web of Science ®Google Scholar
• Schiegl, M. (2004). Simulation. Handbuch zur Schadenreservierung [Handbook on Loss Reserving]. Karlsruhe: Verlag Versicherungswirtschaft.
   Google Scholar
• Schiegl, M. (2015). A model study about the applicability of the chain ladder method. Scandinavian Actuarial Journal 2015(6), 482–499.
   Web of Science ®Google Scholar
• Singh, K. (1998). Breakdown theory for bootstrap quantiles. The Annals of Statistics 26(5), 1719–1732.
   Web of Science ®Google Scholar
• Stromberg, A.J., (1997). Robust covariance estimates based on resampling. Journal of Statistical Planning and Inference 57(2), 321–334. Robust Statistics and Data Analysis, Part II.
   Web of Science ®Google Scholar
• Taylor, G. C. & Ashe, F. (1983). Second moments of estimates of outstanding claims. Journal of Econometrics 23(1), 37–61.
   Web of Science ®Google Scholar
• Van Aelst, S. & Willems, G. (2013). Fast and robust bootstrap for multivariate inference: The R package FRB. Journal of Statistical Software 53(3), 1–32.
   Web of Science ®Google Scholar
• Venter, G. G. (2006). Discussion of the mean square error of prediction in the chain ladder reserving method. ASTIN Bulletin 36, 566–571.
   Web of Science ®Google Scholar
• Verdonck, T. & Debruyne, M. (2011). The influence of individual claims on the chain-ladder estimates: Analysis and diagnostic tool. Insurance: Mathematics and Economics 48(1), 85–98.
   Web of Science ®Google Scholar
• Verdonck, T. & Van Wouwe, M. (2011). Detection and correction of outliers in the bivariate chain-ladder method. Insurance: Mathematics and Economics 49(2), 188–193.
   Web of Science ®Google Scholar
• Verdonck, T., Wouwe, M. V. & Dhaene, J. (2009). A robustification of the chain-ladder method. Nort American Actuarial Journal 13(2), 280–298.
   Google Scholar
• Verrall, R. (1991a). On the estimation of reserves from loglinear models. Insurance: Mathematics and Economics 10(1), 75–80.
   Web of Science ®Google Scholar
• Verrall, R. J. (1991b). Chain ladder and maximum likelihood. Journal of the Institute of Actuaries 118(03), 489–499.
   Google Scholar
• Verrall, R. (2000). An investigation into stochastic claims reserving models and the chain-ladder technique. Insurance: Mathematics and Economics 26(1), 91–99.
   Web of Science ®Google Scholar
• Wüthrich, M.V. & Merz, M., (2008). Stochastic claims reserving methods in insurance, Vol. 435, Chichester: John Wiley & Sons.
   Google Scholar
• Wüthrich, M. V., Merz, M. & Bühlmann, H. (2008). Bounds on the estimation error in the chain ladder method. Scandinavian Actuarial Journal 2008(4), 283–300.
   Web of Science ®Google Scholar
• Wüthrich, M. V., Merz, M. & Lysenko, N. (2009). Uncertainty of the claims development result in the chain ladder method. Scandinavian Actuarial Journal 2009(1), 63–84.
   Web of Science ®Google Scholar