Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T04:57:05.993Z Has data issue: false hasContentIssue false
  • English
  • Français

A NEURAL NETWORK BOOSTED DOUBLE OVERDISPERSED POISSON CLAIMS RESERVING MODEL

Published online by Cambridge University Press:  17 December 2019

Andrea Gabrielli
Andrea Gabrielli*
Affiliation:
RiskLab, Department of Mathematics, ETH Zurich, E-MAIL: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an actuarial claims reserving technique that takes into account both claim counts and claim amounts. Separate (overdispersed) Poisson models for the claim counts and the claim amounts are combined by a joint embedding into a neural network architecture. As starting point of the neural network calibration, we use exactly these two separate (overdispersed) Poisson models. Such a nested model can be interpreted as a boosting machine. It allows us for joint modeling and mutual learning of claim counts and claim amounts beyond the two individual (overdispersed) Poisson models.

Keywords

Cross-classified overdispersed Poisson modelclaims reserving in insurancechain–ladder reservesneural networkembeddingclaim countsclaim amountslearning across portfoliosboosting
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 1 , January 2020 , pp. 25 - 60
Copyright
© Astin Bulletin 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bahdanau, D., Cho, K. and Bengio, Y. (2014) Neural machine translation by jointly learning to align and translate. arXiv 1409.0473, Version of May 19, 2016.Google Scholar
Bengio, Y., Ducharme, R., Vincent, P. and Jauvin, C. (2003) A neural probabilistic language model. Journal of Machine Learning Research, 3, 1137–1155.Google Scholar
Cho, K., van Merrienboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H. and Bengio, Y. (2014) Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv 1406.1078, Version of September 3, 2014.Google Scholar
Cybenko, G. (1989) Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signal, and Systems, 2, 303–314.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
Gabrielli, A., Richman, R. and Wüthrich, M.V. (2018) Neural network embedding of the over-dispersed Poisson reserving model. SSRN Manuscript ID 3288454, Version of November 21, 2018.CrossRefGoogle Scholar
Gabrielli, A. and Wüthrich, M.V. (2018) An individual claims history simulation machine. Risks, 6(2), 29.CrossRefGoogle Scholar
Goodfellow, I., Bengio, Y. and Courville, A. (2016) Deep Learning. MIT Press.Google Scholar
Hachemeister, C.A. and Stanard, J.N. (1975) IBNR claims count estimation with static lag functions. ASTIN Colloquium 1975, Portugal.Google Scholar
Hansen, L.K. and Salamon, P. (1990) Neural network ensembles. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10, 993–1001.CrossRefGoogle Scholar
He, K., Zhang, X. Ren, S. and Sun, J. (2016) Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 770–778.CrossRefGoogle Scholar
Hornik, K., Stinchcombe, M. and White, H. (1989) Multilayer feedforward networks are universal approximators. Neural Networks, 2, 359–366.CrossRefGoogle Scholar
Ioffe, S. and Szegedy, C. (2015) Batch normalization: Accelerating deep network training by reducing internal covariate shift. Proceedings of Machine Learning Research, 37, 448–456.Google Scholar
James, G., Witten, D., Hastie, T. and Tibshirani, R. (2013) An Introduction to Statistical Learning with Applications in R. Springer.CrossRefGoogle Scholar
Kremer, E. (1985) Einführung in die Versicherungsmathematik. Vandenhoek & Ruprecht.Google Scholar
Kuo, K. (2019) DeepTriangle: A deep learning approach to loss reserving. Risks, 7(3), 97.CrossRefGoogle Scholar
LeCun, Y., Bengio, Y. and Hinton, G. (2015) Deep learning. Nature, 521(7553), 436–444.CrossRefGoogle ScholarPubMed
Luong, M.-T., Pham, H. and Manning, C.D. (2015) Effective approaches to attention-based neural machine translation. Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing, pp. 1412–1421.CrossRefGoogle Scholar
Mack, T. (1991) A simple parametric model for rating automobile insurance or estimating IBNR claims reserves. ASTIN Bulletin, 21(1), 93–109.CrossRefGoogle Scholar
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213–225.CrossRefGoogle Scholar
Martinez-Miranda, M.D., Nielsen, J.P. and Verrall, R. (2012) Double chain ladder. ASTIN Bulletin, 42(1), 59–76.Google Scholar
McCullagh, P. and Nelder, J.A. (1983) Generalized Linear Models. Chapman and Hall.CrossRefGoogle Scholar
Mnih, V., Heess, N., Graves, A. and Kavukcuoglu, K. (2014) Recurrent models of visual attention. In: Advances in Neural Information Processing Systems, 27, 2204–2212.Google Scholar
Nelder, J.A. and Wedderburn, R.W.M. (1972) Generalized linear models. Journal of the Royal Statistical Society. Series A (General), 135(3), 370–384.CrossRefGoogle Scholar
R Core Team (2018) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria.Google Scholar
Renshaw, A.E. and Verrall, R.J. (1998) A stochastic model underlying the chain-ladder technique. British Actuarial Journal, 4, 903–923.CrossRefGoogle Scholar
Richman, R. (2018) AI in actuarial science. SSRN Manuscript ID 3218082, Version of August 20, 2018.CrossRefGoogle Scholar
Schmidhuber, J. (2015) Deep learning in neural networks: An overview. Neural Networks, 61, 85–117.CrossRefGoogle ScholarPubMed
Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I. and Salakhutdinov, R. (2014) Dropout: A simple way to prevent neural networks from overfitting. Journal of Machine Learning Research, 15, 1929–1958.Google Scholar
Taylor, G. (2015) Bayesian chain ladder models. ASTIN Bulletin, 45(1), 75–99.CrossRefGoogle Scholar
Wüthrich, M.V. and Merz, M. (2015) Stochastic claims reserving manual: Advances in dynamic modeling. SSRN Manuscript ID 2649057, Version of August 21, 2015.CrossRefGoogle Scholar
Wüthrich, M.V. and Merz, M. (2019) Editorial: Yes, we CANN! ASTIN Bulletin, 49(1), 1–3.CrossRefGoogle Scholar
Supplementary material: File

Gabrielli supplementary material

Gabrielli supplementary material

Download Gabrielli supplementary material(File)
File 1.1 MB