Bridging Structured Knowledge and Data: A Unified Framework with Finance Applications

2026-04-01

AI Summary

This study addresses the challenge of effectively integrating structured prior knowledge—such as economic theory or cross-domain information—into data-driven neural networks to enhance theoretical consistency, interpretability, and generalization. The authors propose Structured Knowledge-Informed Neural Networks (SKINNs), which embed theoretical constraints via differentiable regularization terms, jointly estimate network weights and economically meaningful structural parameters, and enforce global theoretical consistency through collocation points. This framework unifies functional GMM, Bayesian updating, transfer learning, and physics-informed neural networks within an M-estimation setting that achieves root-n convergence, robust covariance estimation, and consistent recovery of pseudo-true parameters. Notably, it establishes, for the first time under high model flexibility, the identifiability of structural parameters. Applied to option pricing, SKINNs significantly improve out-of-sample valuation and hedging performance—especially over long horizons and in high-volatility regimes—while stably recovering economically interpretable parameters.

Abstract

We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function approximation. SKINNs jointly estimate neural network parameters and economically meaningful structural parameters in a single optimization problem, enforcing theoretical consistency not only on observed data but over a broader input domain through collocation, and therefore nesting approaches such as functional GMM, Bayesian updating, transfer learning, PINNs, and surrogate modeling. SKINNs define a class of M-estimators that are consistent and asymptotically normal with root-N convergence, sandwich covariance, and recovery of pseudo-true parameters under misspecification. We establish identification of structural parameters under joint flexibility, derive generalization and target-risk bounds under distributional shift in a convex proxy, and provide a restricted-optimal characterization of the weighting parameter that governs the bias-variance tradeoff. In an illustrative financial application to option pricing, SKINNs improve out-of-sample valuation and hedging performance, particularly at longer horizons and during high-volatility regimes, while recovering economically interpretable structural parameters with improved stability relative to conventional calibration. More broadly, SKINNs provide a general econometric framework for combining model-based reasoning with high-dimensional, data-driven estimation.

Problem

• structured knowledge
• neural networks
• theoretical consistency
• structural parameters
• data-driven estimation

Innovation

• Structured Knowledge
• Neural Networks
• M-estimation
• Collocation
• Econometric Integration