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THE IMPACTS OF INDIVIDUAL INFORMATION ON LOSS RESERVING

Published online by Cambridge University Press:  14 December 2020

Zhigao Wang Open the ORCID record for Zhigao Wang [Opens in a new window] ,
Xianyi Wu  and
Chunjuan Qiu
Zhigao Wang
Affiliation:
Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal UniversityShanghai, China E-Mail: wangzhigao2015@163.com
Xianyi Wu
Affiliation:
Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal UniversityShanghaiChina E-Mail: xywu@stat.ecnu.edu.cn
Chunjuan Qiu*
Affiliation:
Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal UniversityShanghai, China E-Mail: cjqiu@stat.ecnu.edu.cn
*
E-Mail: cjqiu@stat.ecnu.edu.cn
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Abstract

The projection of outstanding liabilities caused by incurred losses or claims has played a fundamental role in general insurance operations. Loss reserving methods based on individual losses generally perform better than those based on aggregate losses. This study uses a parametric individual information model taking not only individual losses but also individual information such as age, gender, and so on from policies themselves into account. Based on this model, this study proposes a computation procedure for the projection of the outstanding liabilities, discusses the estimation and statistical properties of the unknown parameters, and explores the asymptotic behaviors of the resulting loss reserving as the portfolio size approaching infinity. Most importantly, this study demonstrates the benefits of individual information on loss reserving. Remarkably, the accuracy gained from individual information is much greater than that from considering individual losses. Therefore, it is highly recommended to use individual information in loss reserving in general insurance.

Keywords

General insuranceindividual dataloss reservingIBNR and RBNS claimsasymptotic analysis
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 303 - 347
Copyright
© 2020 by Astin Bulletin. All rights reserved

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References

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.CrossRefGoogle Scholar
Avanzi, B., Wong, B. and Yang, X. (2016) A micro-level claim count model with overdispersion and reporting delays. Insurance: Mathematics and Economics, 71, 1–14.Google Scholar
Badescu, A.L., Lin, X.S. and Tang, D. (2016) A marked Cox model for the number of IBNR claims: Theory. Insurance: Mathematics and Economics, 69, 29–37.Google Scholar
Boj, E. and Costa, T. (2018) Logistic classification for new policyholders taking into account prediction error. In Mathematical and Statistical Methods for Actuarial Sciences and Finance, pp. 161–165. Springer.Google Scholar
Crevecoeur, J., Antonio, K. and Verbelen, R. (2019) Modeling the number of hidden events subject to observation delay. European Journal of Operational Research, 277(3), 930–944.CrossRefGoogle Scholar
Denuit, M., Maréchal, X., Pitrebois, S. and Walhin, J.F. (2007) Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems. London: John Wiley & Sons.CrossRefGoogle Scholar
England, P.D. and Verrall, R.J. (2002) Stochastic claims reserving in general insurance. British Actuarial Journal, 8(3), 443–518.CrossRefGoogle Scholar
England, P.D. and Verrall, R.J. (2006) Predictive distributions of outstanding liabilities in general insurance. Annals of Actuarial Science, 1(2), 221–270.CrossRefGoogle Scholar
Fung, T.C., Badescu, A. and Lin, X.S. (2020) A new class of severity regression models with an application to IBNR prediction. North American Actuarial Journal. doi: 10.1080/10920277.2020.1729813.CrossRefGoogle Scholar
Gabrielli, A. and Wüthrich, V.M. (2018) An individual claims history simulation machine. Risks, 6(2), 29.CrossRefGoogle Scholar
Ghalanos, A. and Theussl, S. (2015) Rsolnp: General Non-Linear Optimization Using Augmented Lagrange Multiplier Method. R package version 1.16.Google Scholar
Godecharle, E. and Antonio, K. (2015) Reserving by conditioning on markers of individual claims: A case study using historical simulation. North American Actuarial Journal, 19(4), 273–288.CrossRefGoogle Scholar
Gogol, D. (1993) Using expected loss ratios in reserving. Insurance: Mathematics and Economics, 12(3), 297–299.Google Scholar
Heras, A., Moreno, I. and Vilar-Zanón, J.L. (2018) An application of two-stage quantile regression to insurance ratemaking. Scandinavian Actuarial Journal, 2018(9), 753–769.CrossRefGoogle Scholar
Hesselager, O. (1995) Modelling of discretized claim numbers in loss reserving. ASTIN Bulletin: The Journal of the IAA, 25(2), 119–135.CrossRefGoogle Scholar
Huang, J., Qiu, C. and Wu, X. (2015a) Stochastic loss reserving in discrete time: Individual vs. aggregate data models. Communications in Statistics-Theory and Methods, 44(10), 2180–2206.CrossRefGoogle Scholar
Huang, J., Qiu, C., Wu, X. and Zhou, X. (2015b) An individual loss reserving model with independent reporting and settlement. Insurance: Mathematics and Economics, 64, 232–245.Google Scholar
Huang, J., Wu, X. and Zhou, X. (2016) Asymptotic behaviors of stochastic reserving: Aggregate versus individual models. European Journal of Operational Research, 249(2), 657–666.CrossRefGoogle Scholar
Jewell, W.S. (1989) Predicting IBNYR events and delays: I. continuous time. ASTIN Bulletin: The Journal of the IAA, 19(1), 25–55.CrossRefGoogle Scholar
Jewell, W.S. (1990) Predicting IBNYR events and delays II. Discrete time. ASTIN Bulletin: The Journal of the IAA, 20(1), 93–111.CrossRefGoogle Scholar
Kuo, K. (2019). Deep Triangle: A deep learning approach to loss reserving. Risks, 7(3), 97.CrossRefGoogle Scholar
Larsen, C.R. (2007). An individual claims reserving model. ASTIN Bulletin: The Journal of the International Actuarial Association, 37(01), 113–132.CrossRefGoogle 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.CrossRefGoogle Scholar
Norberg, R. (1993). Prediction of outstanding liabilities in non-life insurance 1. ASTIN Bulletin: The Journal of the IAA, 23(1), 95–115.CrossRefGoogle Scholar
Norberg, R. (1999). Prediction of outstanding liabilities II. Model variations and extensions. ASTIN Bulletin: The Journal of the IAA, 29(1), 5–25.CrossRefGoogle Scholar
Pigeon, M., Antonio, K. and Denuit, M. (2013). Individual loss reserving with the multivariate skew normal framework. ASTIN Bulletin: The Journal of the IAA, 43(3), 399–428.CrossRefGoogle Scholar
Pigeon, M., Antonio, K. and Denuit, M. (2014). Individual loss reserving using paid-incurred data. Insurance: Mathematics and Economics, 58, 121–131.Google Scholar
van der Vaart, A.W. (2000). Asymptotic Statistics. New York: Cambridge University Press.Google Scholar
Verbelen, R., Antonio, K., Claeskens, G. and Crèvecoeur, J. (2017). Predicting daily IBNR claim counts using a regression approach for the occurrence of claims and their reporting delay. Working paper. Available at https://lirias.kuleuven.be/handle/123456789/580750.Google Scholar
Verrall, R.J. (2000). An investigation into stochastic claims reserving models and the chain-ladder technique. Insurance: Mathematics and Economics, 26(1), 91–99.Google Scholar
Verrall, R.J. and Wüthrich, M.V. (2016). Understanding reporting delay in general insurance. Risks, 4(3), 25.CrossRefGoogle Scholar
White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica: Journal of the Econometric Society, 50, 1–25.CrossRefGoogle Scholar
Wüthrich, M.V. (2018). Machine learning in individual claims reserving. Scandinavian Actuarial Journal, 2018(6), 465–480.CrossRefGoogle Scholar
Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. West Sussex: John Wiley & Sons.Google Scholar
Yu, X. and He, R. (2016). Individual claims reserving models based on marked Cox processes (in Chinese). Chinese Journal of Applied Probability and Statistics, 32(2), 201–219.Google Scholar
Zhao, X. and Zhou, X. (2010). Applying copula models to individual claim loss reserving methods. Insurance: Mathematics and Economics, 46(2), 290–299.Google Scholar