Grouping of contracts in insurance using neural networks

ABSTRACT

Despite the high importance of grouping in practice, there exists little research on the respective topic. The present work presents a framework for grouping and a novel method to optimize model points in life insurance. We introduce a supervised clustering algorithm using neural networks to form a less complex portfolio, alias grouping. In a two-step approach, we first approximate selected characteristics of a portfolio. Next, we nest this estimator in a neural network, such that cluster representatives, alias model points, are calibrated in accordance with their effect on the characteristics of the portfolio. This approach is similar to the work by Horvath, B., Muguruza, A. & Tomas, M. [(2019). Deep learning volatility. Available on arXiv 1901.09647.], who focus on the calibration of implied volatility models. Our numerical experiments for term life insurance and defined contribution pension plans show significant improvements, in terms of capturing the characteristics of a portfolio, of the neural network approach over K-means clustering, a common baseline algorithm for grouping. These results are further confirmed by a sensitivity analysis of the investment surplus, where we additionally show the flexibility of the model to include common industry practice.

Keywords:

• Grouping
• term life insurance
• defined contribution plan
• non-linear optimization
• neural networks
• bagging
• LSTM
• K-means clustering
• supervised learning

Acknowledgments

The authors would also like to thank Ralf Korn, who stimulated the extension of our research to pension plans. Furthermore, the authors gratefully acknowledge useful comments of Hans-Joachim Zwiesler and Anselm Haselhoff during the preparation of the paper. Lastly, we thank the reviewer for their constructive remarks.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 To be precise, the age of retirement in Germany varies between 65 and 67 based on the date of birth. The basic retirement at 67 applies for individuals born on 1 January 1964 or later, see Federal Ministry of Labour and Social Affairs (2019).

2 The given probabilities are in line with the pension plan service table in Dickson et al. (2009), Table 10.2.

Additional information

Funding

This work was supported by Ministerium für Kultur und Wissenschaft des Landes Nordrhein-Westfalen and their grant ‘FH BASIS 2019’ (reference 1908fhb005).