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COMPOUND POISSON CLAIMS RESERVING MODELS: EXTENSIONS AND INFERENCE

Published online by Cambridge University Press:  11 May 2018

Shengwang Meng  and
Guangyuan Gao
Shengwang Meng
Affiliation:
Center for Applied Statistics and School of Statistics, Renmin University of China, Beijing 100872, China, E-Mail: [email protected]
Guangyuan Gao*
Affiliation:
Center for Applied Statistics and School of Statistics, Renmin University of China, Beijing 100872, China
*
E-Mail: [email protected]
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Abstract

We consider compound Poisson claims reserving models applied to the paid claims and to the number of payments run-off triangles. We extend the standard Poisson-gamma assumption to account for over-dispersion in the payment counts and to account for various mean and variance structures in the individual payments. Two generalized linear models are applied consecutively to predict the unpaid claims. A bootstrap is used to estimate the mean squared error of prediction and to simulate the predictive distribution of the unpaid claims. We show that the extended compound Poisson models make reasonable predictions of the unpaid claims.

Keywords

Stochastic claims reservingcompound Poisson modelgeneralized linear modelquasi-likelihood estimationbootstrapTweedie's distribution
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 3 , September 2018 , pp. 1137 - 1156
Copyright
Copyright © Astin Bulletin 2018 

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References

Antonio, K. and Plat, R. (2014) Micro-level stochastic loss reserving for general insurance. Scandinavian Actuarial Journal, 2014, 649–669.Google 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, 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
Boucher, J.-P. and Davidov, D. (2011) On the importance of dispersion modeling for claims reserving: An application with the Tweedie distribution. Variance, 5, 158–172.Google Scholar
England, P.D. and Verrall, R.J. (2002) Stochastic claims reserving in general insurance. British Actuarial Journal, 8, 443–518.Google Scholar
Gigante, P., Picech, L. and Sigalotti, L. (2013) Claims reserving in the hierarchical generalized linear model framework. Insurance: Mathematics and Economics, 52, 381–390.Google Scholar
Gigante, P., Picech, L. and Sigalotti, L. (2016) A mixture model for payments and payment numbers in claims reserving. ASTIN Bulletin, 47, 1–29.Google Scholar
Klugman, S.A., Panjer, H.H. and Willmot, G.E. (2012) Loss Models: From Data to Decisions, 4th ed. New York: John Wiley & Sons.Google Scholar
Lee, Y. and Nelder, J.A. (2001) Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions. Biometrika, 88, 987–1006.Google Scholar
Martínez-Miranda, M.D., Nielsen, B., Nielsen, J.P. and Verrall, R. (2011) Cash flow simulation for a model of outstanding liabilities based on claim amounts and claim numbers. ASTIN Bulletin, 41, 107–129.Google Scholar
Martínez-Miranda, M.D., Nielsen, J.P. and Verrall, R. (2012) Double chain ladder. ASTIN Bulletin, 42, 59–76.Google Scholar
Martínez-Miranda, M.D., Nielsen, J.P. and Verrall, R. (2013) Double chain ladder and Bornhuetter–Ferguson. North American Actuarial Journal, 17, 101–113.Google Scholar
Martínez-Miranda, M.D., Nielsen, J.P., Verrall, R. and Wüthrich, M.V. (2015) Double chain ladder, claims development inflation and zero-claims. Scandinavian Actuarial Journal, 2015, 383–405.Google Scholar
McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models, 2nd ed. New York: Chapman & Hall.Google Scholar
Norberg, R. (1993) Prediction of outstanding liabilities in non-life insurance. ASTIN Bulletin, 23, 95–115.Google Scholar
Peters, G.W., Shevchenko, P.V. and Wüthrich, M.V. (2009) Model uncertainty in claims reserving within Tweedie's compound Poisson models. ASTIN Bulletin, 39, 1–33.Google Scholar
Renshaw, A.E. and Verrall, R.J. (1998) A stochastic model underlying the chain-ladder technique. British Actuarial Journal, 4, 903–923.Google Scholar
Smyth, G.K. and Jørgensen, B. (2002) Fitting Tweedie's compound Poisson model to insurance claims data: Dispersion modelling. ASTIN Bulletin, 32, 143–157.Google Scholar
Taylor, G. (2000) Loss Reserving: An Actuarial Perspective. Huebner International Series on Risk, Insurance and Economic Security. Boston: Kluwer Academic Publishers.Google Scholar
Taylor, G. and Xu, J. (2016) An empirical investigation of the value of finalisation count information to loss reserving. Variance, 10, 75–120.Google Scholar
Verrall, R., Nielsen, J.P. and Jessen, A.H. (2010) Prediction of RBNS and IBNR claims using claim amounts and claim counts. ASTIN Bulletin, 40, 871–887.Google Scholar
Verrall, R.J. and Wüthrich, M.V. (2016) Understanding reporting delay in general insurance. Risks, 4, 25.Google Scholar
Wright, T.S. (1990) A stochastic method for claims reserving in general insurance. Journal of the Institute of Actuaries, 117, 677–731.Google Scholar
Wüthrich, M.V. (2003) Claims reserving using Tweedie's compound Poisson model. ASTIN Bulletin, 33, 331–346.Google Scholar
Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Chichester: John Wiley & Sons.Google Scholar
Wüthrich, M.V. and Merz, M. (2015) Stochastic claims reserving manual: Advances in dynamic modeling. Swiss Finance Institute Research Paper no. 15–34.Google Scholar