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

Donatien Hainaut ()
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Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2024042, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

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 networks; variable annuities; Feynman-Kac equation; life insurance (search for similar items in EconPapers)
Pages: 32
Date: 2024-05-13
Note: In: Annals of Actuarial Science, 2024, vol. 18(2), p. 442-473
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2024042

DOI: 10.1017/S1748499524000095

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