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

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

No 2023029, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: Guaranteed Minimum Accumulation Benefits (GMAB) are retirement savings vehicles which protect the policyholder against downside market risk. This article proposes a valuation method of these contracts based on physics inspired neural networks (PINN's), in 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) ruling the GMAB price in an arbitrage-free market. In our context, the FK PDE depends on multiple variables and is hard to solve by classical finite difference approximations. In comparison, PINN's constitute a efficient alternative which furthermore can evaluate GMAB's with various specifications without retraining. To illustrate this, we consider a market with four risk factors. We first find a closed form expression for the GMAB that serves as benchmark for the PINN. Next, we propose a scaled version of the FK equation that we solve with a PINN. Pricing errors are analyzed in a numerical illustration.

Pages: 29
Date: 2023-09-18
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