Grouping of contracts in insurance using neural networks

References

• Aleandri, M. (2017). Modeling dynamic policyholder behavior through machine learning techniques. Submitted to Scuola di Scienze Statistiche.
   Google Scholar
• Badirli, S., Liu, X., Xing, Z., Bhowmik, A., Doan, K. & Keerthi, S. (2020). Gradient boosting neural networks: GrowNet. arXiv: 2002.07971.
   Google Scholar
• Bengio, Y. (2012). Practical recommendations for gradient-based training of deep architectures. Available on arXiv 1206.5533.
   Google Scholar
• Bettels, C., Fabrega, J. & Weiß, C. (2014a). Anwendung von Least Squares Monte Carlo (LSMC) Solvency-II-Kontext - Teil 1. Der Aktuar 2, 85–91.
   Google Scholar
• Bettels, C., Fabrega, J. & Weiß, C. (2014b). Anwendung von Least Squares Monte Carlo (LSMC) Solvency-II-Kontext - Teil 2. Der Aktuar 3, 151–155.
   Google Scholar
• Blanchet-Scalliet, C., Dorobantu, D. & Salhi, Y. (2017). A Model-Point Approach to Indifference Pricing on Life Insurance Portfolios with Dependent Lives. Methodology And Computing In Applied Probability, 21, 423–448. doi: 10.1007/s11009-017-9611-2
   Web of Science ®Google Scholar
• Borovkov, A. (2013). Probability theory.. Universitext. London: Springer London. ISBN: 978-1-4471-5201-9.
   Google Scholar
• Burkhart, T. (2018). Surrender risk in the context of the quantitative assessment of participating life insurance contracts under solvency II. Risks 6(3), 66. doi: 10.3390/risks6030066
   Web of Science ®Google Scholar
• Chollet, F. et al. 2015). Keras. https://keras.io.
   Google Scholar
• Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals and Systems 2, 303–314. doi: 10.1007/BF02551274
   Google Scholar
• DAV-Arbeitsgruppe (2010). Best Estimate in der Lebensversicherung (2010).
   Google Scholar
• DAV. Höchstrechnungszins in der Lebensversicherung. https://aktuar.de/unsere-themen/lebensversicherung/hoechstrechnungszins/Seiten/default.aspx. Accessed December 3, 2019.
   Google Scholar
• Denuit, M. & Trufin, J. (2015). Model points and tail-VaR in life insurance. Insurance: Mathematics and Economics 64(C), 268–272.
   Web of Science ®Google Scholar
• Deprez, P., Shevchenko, P. V. & Wüthrich, M. V. (2017). Machine learning techniques for mortality modeling. European Actuarial Journal 7(2), 337–352. doi: 10.1007/s13385-017-0152-4
   Web of Science ®Google Scholar
• Dickson, D. C., Hardy, M. R. & Waters, H. R. (2009) Actuarial mathematics for life contingent risks. International Series on Actuarial Science. Cambridge: Cambridge University Press.
   Google Scholar
• Dugas, C., Bengio, Y., Chapados, N., Vincent, P., Denoncourt, G. & Fournier, C. (2003). Statistical learning algorithms applied to automobile insurance ratemaking. Intelligent and Other Computational Techniques in Insurance, 6, 137–197. doi: 10.1142/9789812794246_0004
   Google Scholar
• Führer, C. & Grimmer, A. (2010). Einführung in die lebensversicherungsmathematik. (2nd ed.). Karlsruhe: Verlag Versicherungswirtschaft GmbH.
   Google Scholar
• Federal Ministry of Labour and Social Affairs. Old-age pensions. https://www.bmas.de/EN/Our-Topics/Pensions/old-age-pensions.html. Accessed June 27, 2019.
   Google Scholar
• Frostig, E. (2001). A comparison between homogeneous and heterogeneous portfolios. Insurance: Mathematics and Economics 29(1), 59–71.
   Web of Science ®Google Scholar
• GDV (2019). Statistical yearbook of German insurance 2018. Berlin: GDV.
   Google Scholar
• Glasserman, P. (2004). Monte carlo methods in financial engineering. New York: Springer.
   Google Scholar
• Goffard, P.-O. & Guerrault, X. (2015). Is it optimal to group policyholders by age, gender, and seniority for BEL computations based on model points?. European Actuarial Journal 5, 165–180. doi: 10.1007/s13385-015-0106-7
   Web of Science ®Google Scholar
• Goodfellow, I., Bengio, Y. & Courville, A. (2016). Deep learning. Cambridge: MIT Press.
   Google Scholar
• Hagan, M. T., Demuth, H. B., Beale, M. H. & De Jesus, O. (2014). Neural network design. 2nd ed.
   Google Scholar
• Hejazi, S. A. & Jackson, K. R. (2016). Efficient valuation of SCR via a neural network approach. Available at: arXiv 1610.01946.
   Google Scholar
• Hochreiter, S. & Schmidhuber, J. (1997). Long short-term memory. Neural Computation 9, 1735–80. doi: 10.1162/neco.1997.9.8.1735
   PubMed Web of Science ®Google Scholar
• Hornik, K. (1991). Approximation capabilities of multilayer feedforward networks. Neural Networks 4, 251–257. doi: 10.1016/0893-6080(91)90009-T
   Web of Science ®Google Scholar
• Horvath, B., Muguruza, A. & Tomas, M. (2019). Deep learning volatility. Available at: arXiv 1901.09647.
   Google Scholar
• Kiermayer, M. (2019). Replicating life insurance business using neural networks. MA thesis. Ulm: Ulm University.
   Google Scholar
• Kingma, D. & Ba, J. (2015). Adam: A method for stochastic optimization. International Conference on Learning Representation.
   Google Scholar
• Krah, A.-S. (2019). Machine learning in least-squares Monte Carlo proxy modeling of life insurance companies. PhD thesis. Kaiserslautern: TU Kaiserslautern.
   Google Scholar
• Krah, A.-S., Nikolic, Z. & Korn, R. (2018). A least-squares Monte Carlo framework in proxy modeling of life insurance companies. Risks 6(2), 62. doi: 10.3390/risks6020062
   Web of Science ®Google Scholar
• Leitschkis, M., Hörig, M., Ketterer, F. & Bettels, C. (2013). Least squares Monte Carlo for fast and robust capital projections. Milliman White Paper. https://de.milliman.com/
   Google Scholar
• Milhaud, X. & Dutang, C. (2018). Lapse tables for lapse risk management in insurance: a competing risk approach. European Actuarial Journal 8(1), 97–126. doi: 10.1007/s13385-018-0165-7
   Web of Science ®Google Scholar
• Nörtemann, S. (2012). Das Laufzeitproblem bei stochastischen Projektionsrechnungen. DAA Workshop Für Junge Mathematiker 9.
   Google Scholar
• Neuburger, E., Brans, N., Gohdes, A., Hirschberg-Tafel, M., Rhiel, R. & Schäfferling, K. (1997). Mathematik und Technik betrieblicher Pensionszusagen. Schriftenreihe Angewandte Versicherungsmathematik (25). Versicherungswirtschaft e.V..
   Google Scholar
• Penschinski, B. & Alexin, J. (2016). Validierungsapparat für Modellpunktverdichtung in stoch. ALM - Modellen und Heuristik zur Optimierung verdichteter Ablaufleistungen. Der Aktuar 1, 6–11.
   Google Scholar
• Richman, R. & Wüthrich, M. V. (2018). A neural network extension of the Lee-Carter model to multiple populations. Available at: SSRN 3270877.
   Google Scholar
• Selvaraju, R. R., Das, A., Vedantam, R., Cogswell, M., Parikh, D. & Batra, D. (2016). Grad-CAM: Visual explanations from deep networks via gradient-based localization. Available at: arXiv 1610.02391.
   Google Scholar
• Statistik Bundesagentur für Arbeit (2018). Tabellen, Beschäftigte nach Altersgruppen (Zeitreihe Quartalszahlen). www.statistik.arbeitsagentur.de. Accessed September 3, 2020.
   Google Scholar
• Statistisches Bundesamt (2020). Lohn- und Einkommensteuer 2016, Table A 3, p. 9. www.destatis.de. Accessed September 3, 2020.
   Google Scholar
• Vaswani, A., Shazeer, N., Parmas, N., Uszkoreit, J., Jones, L., Gomez, A., Kaiser, L. & Polosukhin, I. (2017). Attention is all you need. Advances in Neural Information Processing Systems 30, 6000–6010.
   Google Scholar
• Wüthrich, M. V. (2018). Neural networks applied to chain–ladder reserving. European Actuarial Journal 8. doi: 10.1007/s13385-018-0184-4
   Web of Science ®Google Scholar
• Wiese, M., Knobloch, R., Korn, R. & Kretschmer, P. (2019). Quant GANs: deep generation of financial time series. Available at: arXiv 1907.06673.
   Google Scholar