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Valuation of guaranteed minimum accumulation benefits (GMABs) with physics-inspired neural networks

Published online by Cambridge University Press:  13 May 2024

Donatien Hainaut Open the ORCID record for Donatien Hainaut [Opens in a new window]
Donatien Hainaut*
Affiliation:
UCLouvain, LIDAM, Ottignies-Louvain-la-Neuve, Belgium
*
Corresponding author: Donatien Hainaut; Email: donatien.hainaut@uclouvain.be
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Abstract

Guaranteed minimum accumulation benefits (GMABs) are retirement savings vehicles that protect the policyholder against downside market risk. This article proposes a valuation method for these contracts based on physics-inspired neural networks (PINNs), in the presence of multiple financial and biometric risk factors. A PINN integrates principles from physics into its learning process to enhance its efficiency in solving complex problems. In this article, the driving principle is the Feynman–Kac (FK) equation, which is a partial differential equation (PDE) governing the GMAB price in an arbitrage-free market. In our context, the FK PDE depends on multiple variables and is difficult to solve using classical finite difference approximations. In comparison, PINNs constitute an efficient alternative that can evaluate GMABs with various specifications without the need for retraining. To illustrate this, we consider a market with four risk factors. We first derive a closed-form expression for the GMAB that serves as a benchmark for the PINN. Next, we propose a scaled version of the FK equation that we solve using a PINN. Pricing errors are analyzed in a numerical illustration.

Keywords

Neural networksvariable annuitiesFeynman–Kac equationlife insurance
Type
Original Research Paper
Information
Annals of Actuarial Science , First View , pp. 1 - 32
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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