🤖 AI Summary
This study addresses the high computational cost of asset-liability management (ALM) models in the insurance industry, particularly in large-scale sensitivity analyses and stress testing for solvency capital assessment and asset allocation optimization. It introduces path signature theory into ALM modeling for the first time, approximating key outputs—such as embedded value and best estimate—as linear combinations of path signatures derived from economic scenario trajectories. A regularized linear regression framework is then employed to construct a surrogate model. This approach substantially reduces computational overhead while maintaining high predictive accuracy and demonstrating robustness to shifts in the underlying economic scenario distribution, thereby enabling efficient large-scale balance sheet evaluation and rapid decision support.
📝 Abstract
In the insurance industry, Asset and Liability Management (ALM) models are key tools for numerous applications, including Solvency Capital Requirement (SCR) computation and asset allocation optimization. However, their use often entails a significant computational cost, especially when a large number of sensitivities or stressed balance-sheet evaluations must be performed. In this work, we propose an approximation framework for the outputs of an ALM model, such as the Value In Force or the Best Estimate, based on the theory of path signatures. More precisely, the proposed approach consists of approximating ALM outputs by a linear combination of signature terms derived from input economic scenarios. We show that the resulting surrogate is easy to calibrate, essentially through regularized linear regression, and exhibits strong predictive performance while drastically reducing computational costs. We further investigate its robustness under changes in the distribution of economic scenarios by considering variations in the parameters of the underlying model of risk factors while the surrogate model is kept fixed. These results make the proposed approach particularly suitable for large-scale sensitivity analyses and fast balance-sheet evaluations in practical actuarial applications.