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

Anne-Sophie Krah, Zoran Nikolić and Ralf Korn
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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

Risks, 2020, vol. 8, issue 4, 1-21

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.

Keywords: least-squares Monte Carlo method; proxy modeling; life insurance; Solvency II; neural networks; machine learning; ensemble method (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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