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

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.