Skip to main content
Log in

Modeling paid-ups in life insurance products for risk management

  • Original Article
  • Published:
Risk Management Aims and scope Submit manuscript

Abstract

Life insurance companies are subject to various risks related to universal life products. One such risk-paid-up-arises when policyholders, at some point before maturity, exercise their option to stop paying the periodic premiums initially agreed to for the life of the policy. Here, several predictive models are applied, aimed at anticipating the future state of in-force premium payment policies. This is undertaken in conjunction with balancing techniques, designed to avoid misclassification errors caused by the scarcity of paid-up events in our data. Using the findings from our predictive modeling, we initially identify certain policyholder profiles that seem less likely to paid-up premiums and consequently may be considered as potential targets for underwriting. Additionally, we delve into an essential aspect of policy design: surrender fees. Our analysis highlights a pattern where surrender fees, intended to mitigate surrender risk, may actually exacerbate the risk of policies becoming paid-up under certain circumstances.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Data availability

The data utilized in this article is confidential and proprietary, belonging to an insurance company operating within the Spanish insurance market. As such, it is not publicly available or open source.

Notes

  1. See https://www.cfoforum.eu/embedded_value.html.

  2. As contributions to the SCR are usually the difference between a stressed BEL and the central one, although both depend on several valuation assumptions, such as paid-up probabilities.

References

  • Breiman, L. 1996. Bagging predictors. Machine Learning 24: 123–40.

    Article  Google Scholar 

  • Breiman, L. 2001. Random forests. Machine Learning 45 (1): 5–32.

    Article  Google Scholar 

  • Breiman, L., et al. 1984. Classification and regression trees. Boca Raton: Chapman and Hall/CRC.

    Google Scholar 

  • Campbell, J., et al. 2014. Modelling of policyholder behaviour for life assurance and annuity products. Schaumburg: Society of Actuaries.

    Google Scholar 

  • Chawla, N.V., et al. 2002. SMOTE: Synthetic minority over-sampling technique. Journal of Artificial Intelligent Research 16: 321–57.

    Article  Google Scholar 

  • Chen, T., and C. Guestrin. 2016. Xgboost: a scalable tree boosting system. In: In Proceedings of the 22nd Acm Sigkdd International Conference on Knowledge Discovery and Data Mining, no. 2, 785–794.

  • Eling, M., and M. Kochanski. 2013. Research on lapse in life insurance: what has been done and what needs to be done? The Journal of Risk Finance 14 (4): 392–413.

    Article  Google Scholar 

  • Elkan, C. 2001. The foundations of cost-sensitive learning. In: In Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, 973–978.

  • Estabrooks, A., T. Jo, and N. Japkowicz. 2004. A multiple resampling method for learning from imbalanced data sets. Computational Intelligence 20 (1): 18–36.

    Article  Google Scholar 

  • Fier, S.G., and A.P. Liebenberg. 2013. Life insurance lapse behavior. North American Actuarial Journal 2 (17): 153–167.

    Article  Google Scholar 

  • Friedman, J.H. 2001. Greedy function approximation: A gradient boosting machine. The Annals of Statistics 29 (5): 1189–1232.

    Article  Google Scholar 

  • Gatzert, N., G. Hoermann, and H. Schmeiser. 2009. The impact of the secondary market on life insurers’ surrender profits. Journal of Risk and Insurance 4 (76): 887–908.

    Article  Google Scholar 

  • He, H., and E.A. Garcia. 2009. Learning from imbalanced data. IEEE Transactions on Knowledge and Data Engineering 9 (21): 1263–84.

    Google Scholar 

  • Henriksen, L.F.B., J.W. Nielsen, and M. Steffensen. 2014. Markov chain modeling of policyholder behavior in life insurance and pension. European Actuarial Journey 4: 1–29.

    Article  Google Scholar 

  • Khan, S.H., et al. 2017. Cost-sensitive learning of deep feature representations from imbalanced data. IEEE Transactions on Neural Networks and Learning Systems 8 (29): 3573–3587.

    Google Scholar 

  • Kuhn, M. 2008. Building predictive models in R using the caret package. Journal of Statistical Software 28 (5): 1–26.

    Article  Google Scholar 

  • Ling, C.X., and V.S. Sheng. 2008. Cost-sensitive learning and the class imbalance problem. In Encyclopedia of machine learning, ed. C. Sammut, 231–235. Spring.

    Google Scholar 

  • López, V., et al. 2013. An insight into classification with imbalanced data: Empirical results and current trends on using data intrinsic characteristics. Information Sciences 250: 113–141.

    Article  Google Scholar 

  • Maalouf, M., and M. Siddiqi. 2014. Weighted logistic regression for large-scale imbalanced and rare events data. Knowledge-Based Systems 59: 142–148.

    Article  Google Scholar 

  • Menardi, G., and N. Torelli. 2014. Training and assessing classification rules with imbalanced data. Mining and Knowledge Discovery 1 (28): 92–122.

    Article  Google Scholar 

  • Ramraj, S., et al. 2016. Experimenting XGBoost algorithm for prediction and classification of different datasets. International Journal of Control Theory and Applications 9 (40): 651–662.

    Google Scholar 

  • Russell, D.T., et al. 2013. An empirical analysis of life insurance policy surrender activity. Journal of Insurance Issues 36 (1): 35–57.

    Google Scholar 

  • Seiffert, C. et al. 2007. Mining data with rare events: A case study. In: 19th international conference on tools with artificial intelligence, pp. 132–139.

  • Smith, M.L. 1982. The life insurance policy as an options package. Journal of Risk and Insurance 49: 583–601.

    Article  Google Scholar 

  • Sun, Y., A.K. Wong, and M.S. Kamel. 2009. Classification of imbalanced data: A review. International Journal of Pattern Recognition and Artificial Intelligence 4 (23): 687–719.

    Article  Google Scholar 

  • Thai-Nghe, N., Z. Gantner, and L. Schmidt-Thieme. 2010. Cost-sensitive learning methods for imbalanced data. In: In The 2010 International Joint Conference on Neural Networks (IJCNN), pp. 1–8.

  • Venables, W.N., and B.D. Ripley. 2002. Modern applied statistics with S. New York: Springer.

    Book  Google Scholar 

  • Wallace, B. C. et al. 2011. Class Imbalance, Redux. In: IEEE 11th International Conference on Data Mining, pp. 754–763.

  • Weiss, M. 2004. Mining with rarity. ACM SIGKDD Explorations Newsletter 6 (1): 7–19.

    Article  Google Scholar 

Download references

Funding

Funding was provided by Ministerio de Ciencia, Innovación y Universidades (Grant No. PID2019-105986GB-C21), AGAUR of the Catalan Government (Grant Nos. 2020DI9, 2017SGR1147).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David Anaya.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Anaya, D., Bermúdez, L. & Belles-Sampera, J. Modeling paid-ups in life insurance products for risk management. Risk Manag 26, 15 (2024). https://doi.org/10.1057/s41283-024-00146-4

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1057/s41283-024-00146-4

Keywords

Navigation