Stochastic loss reserving using individual information model with over-dispersed Poisson

References

• 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, 4(1), 7–31. https://doi.org/https://doi.org/10.1017/S1748499500000580
   Google Scholar
• Alai, D. H., Merz, M., & Wüthrich, M. V. (2010). Prediction uncertainty in the Bornhuetter–Ferguson claims reserving method: Revisited. Annals of Actuarial Science, 5(1), 7–7. https://doi.org/https://doi.org/10.1017/S1748499510000023
   Google Scholar
• Antonio, K., & Plat, R. (2014). Micro-level stochastic loss reserving for general insurance. Scandinavian Actuarial Journal, 2014(7), 649–669. https://doi.org/https://doi.org/10.1080/03461238.2012.755938
   Web of Science ®Google Scholar
• Arjas, E. (1989). The claims reserving problem in non-life insurance: Some structural ideas. ASTIN Bulletin: The Journal of the IAA, 19(2), 139–152. https://doi.org/https://doi.org/10.2143/AST.19.2.2014905
   Google Scholar
• Crevecoeur, J., Antonio, K., & Verbelen, R. (2019). Modeling the number of hidden events subject to observation delay. European Journal of Operational Research, 277(3), 930–944. https://doi.org/https://doi.org/10.1016/j.ejor.2019.02.044
   Web of Science ®Google Scholar
• England, P. D., & Verrall, R. J. (2002). Stochastic claims reserving in general insurance. British Actuarial Journal, 8(3), 443–544. https://doi.org/https://doi.org/10.1017/S1357321700003809
   Google Scholar
• Huang, J., Qiu, C., & Wu, X. (2015). Stochastic loss reserving in discrete time: Individual vs. aggregate data models. Communications in Statistics-Theory and Methods, 44(10), 2180–2206. https://doi.org/https://doi.org/10.1080/03610926.2014.976473
   Web of Science ®Google Scholar
• Huang, J., Qiu, C., Wu, X., & Zhou, X. (2015). An individual loss reserving model with independent reporting and settlement. Insurance: Mathematics and Economics, 64(1), 232–245. https://doi.org/https://doi.org/10.1016/j.insmatheco.2015.05.010
   Google Scholar
• Huang, J., Wu, X., & Zhou, X. (2016). Asymptotic behaviors of stochastic reserving: Aggregate versus individual models. European Journal of Operational Research, 249(2), 657–666. https://doi.org/https://doi.org/10.1016/j.ejor.2015.09.039
   Web of Science ®Google Scholar
• Lindholm, M., Lindskog, F., & Wahl, F. (2020). Estimation of conditional mean squared error of prediction for claims reserving. Annals of Actuarial Science, 14(1), 93–128. https://doi.org/https://doi.org/10.1017/S174849951900006X
   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. https://doi.org/https://doi.org/10.2143/AST.23.2.2005092
   Google Scholar
• Mack, T. (2000). Credible claims reserves: The Benktander method. ASTIN Bulletin: The Journal of the IAA, 30(2), 333–347. https://doi.org/https://doi.org/10.2143/AST.30.2.504639
   Google Scholar
• McCullagh, P., & Nelder, J. A. (1989). Generalized linear models (2nd ed). Chapman and Hall.
   Google Scholar
• Norberg, R. (1993). Prediction of outstanding liabilities in non-life insurance 1. ASTIN Bulletin: The Journal of the IAA, 23(1), 95–115. https://doi.org/https://doi.org/10.2143/AST.23.1.2005103
   Google Scholar
• Norberg, R. (1999). Prediction of outstanding liabilities II. Model variations and extensions. ASTIN Bulletin: The Journal of the IAA, 29(1), 5–25. https://doi.org/https://doi.org/10.2143/AST.29.1.504603
   Google Scholar
• Pigeon, M., Antonio, K., & Denuit, M. (2013). Individual loss reserving with the multivariate skew normal framework. ASTIN Bulletin: The Journal of the IAA, 43(3), 399–428. https://doi.org/https://doi.org/10.1017/asb.2013.20
   Web of Science ®Google Scholar
• Pigeon, M., Antonio, K., & Denuit, M. (2014). Individual loss reserving using paid-incurred data. Insurance: Mathematics and Economics, 58(2), 121–131. https://doi.org/https://doi.org/10.1016/j.insmatheco.2014.06.012
   Google Scholar
• Van der Vaart, A. W. (2000). Asymptotic Statistics. Cambridge University Press.
   Google Scholar
• Verrall, R. J., Nielsen, J. P., & Jessen, A. H. (2010). Prediction of RBNS and IBNR claims using claim amounts and claim counts. Astin Bulletin, 40(2), 871–887. https://doi.org/https://doi.org/10.2143/AST.40.2.2061139
   Web of Science ®Google Scholar
• Wahl, F. (2019). Explicit moments for a class of micro-models in non-life insurance. Insurance: Mathematics and Economics, 89(7), 140–156. https://doi.org/https://doi.org/10.1016/j.insmatheco.2019.10.001
   Google Scholar
• Wahl, F., Lindholm, M., & Verrall, R. (2019). The collective reserving model. Insurance: Mathematics and Economics, 87(7), 34–50. https://doi.org/https://doi.org/10.1016/j.insmatheco.2019.04.003
   Google Scholar
• Wüthrich, M. V., & Merz, M. (2008). Stochastic Claims Reserving Methods in Insurance. John Wiley and Sons.
   Google Scholar
• Yu, X., & He, R. (2016). Individual claims reserving models based on marked Cox processes. Chinese Journal of Applied Probability and Statistics 32(2), 201-219. http://aps.ecnu.edu.cn/EN/Y2016/V32/I2/201
   Google Scholar
• Zhao, X., & Zhou, X. (2010). Applying copula models to individual claim loss reserving methods. Insurance: Mathematics and Economics, 46(2), 290–299. https://doi.org/https://doi.org/10.1016/j.insmatheco.2009.11.001
   Web of Science ®Google Scholar