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Least-Squares Monte Carlo for Proxy Modeling in Life Insurance: Neural Networks

Author

Listed:
  • Anne-Sophie Krah

    (Department of Mathematics, TU Kaiserslautern, 67653 Kaiserslautern, Germany)

  • Zoran Nikolić

    (Mathematical Institute, University Cologne, Weyertal 86-90, 50931 Cologne, Germany)

  • Ralf Korn

    (Department of Mathematics, TU Kaiserslautern, 67653 Kaiserslautern, Germany
    Department of Financial Mathematics, Fraunhofer ITWM, 67663 Kaiserslautern, Germany)

Abstract

The least-squares Monte Carlo method has proved to be a suitable approximation technique for the calculation of a life insurer’s solvency capital requirements. We suggest to enhance it by the use of a neural network based approach to construct the proxy function that models the insurer’s loss with respect to the risk factors the insurance business is exposed to. After giving a mathematical introduction to feed forward neural networks and describing the involved hyperparameters, we apply this popular form of neural networks to a slightly disguised data set from a German life insurer. Thereby, we demonstrate all practical aspects, such as the hyperparameter choice, to obtain our candidate neural networks by bruteforce, the calibration (“training”) and validation (“testing”) of the neural networks and judging their approximation performance. Compared to adaptive OLS, GLM, GAM and FGLS regression approaches, an ensemble built of the 10 best derived neural networks shows an excellent performance. Through a comparison with the results obtained by every single neural network, we point out the significance of the ensemble-based approach. Lastly, we comment on the interpretability of neural networks compared to polynomials for sensitivity analyses.

Suggested Citation

  • Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2020. "Least-Squares Monte Carlo for Proxy Modeling in Life Insurance: Neural Networks," Risks, MDPI, vol. 8(4), pages 1-21, November.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:4:p:116-:d:439775
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    References listed on IDEAS

    as
    1. Mark Kiermayer & Christian Wei{ss}, 2019. "Grouping of Contracts in Insurance using Neural Networks," Papers 1912.09964, arXiv.org.
    2. Magnus Wiese & Robert Knobloch & Ralf Korn & Peter Kretschmer, 2020. "Quant GANs: deep generation of financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 20(9), pages 1419-1440, September.
    3. Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2018. "A Least-Squares Monte Carlo Framework in Proxy Modeling of Life Insurance Companies," Risks, MDPI, vol. 6(2), pages 1-26, June.
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    Cited by:

    1. Giulia Di Nunno & Anton Yurchenko-Tytarenko, 2022. "Sandwiched Volterra Volatility model: Markovian approximations and hedging," Papers 2209.13054, arXiv.org, revised Jul 2024.
    2. Vali Asimit & Ioannis Kyriakou & Jens Perch Nielsen, 2020. "Special Issue “Machine Learning in Insurance”," Risks, MDPI, vol. 8(2), pages 1-2, May.
    3. Nelson Kemboi Yego & Juma Kasozi & Joseph Nkurunziza, 2021. "A Comparative Analysis of Machine Learning Models for the Prediction of Insurance Uptake in Kenya," Data, MDPI, vol. 6(11), pages 1-17, November.
    4. Borgonovo, Emanuele & Clemente, Gian Paolo & Rabitti, Giovanni, 2024. "Why insurance regulators need to require sensitivity settings of internal models for their approval," Finance Research Letters, Elsevier, vol. 60(C).
    5. Shuai Yang & Kenneth Q. Zhou, 2023. "On Risk Management of Mortality and Longevity Capital Requirement: A Predictive Simulation Approach," Risks, MDPI, vol. 11(12), pages 1-18, November.

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