Bridging Structured Knowledge and Data: A Unified Framework with Finance Applications
This provides a general econometric framework for combining model-based reasoning with high-dimensional data, addressing a domain-specific need in finance and related fields, though it builds incrementally on existing methods like PINNs and GMM.
The authors tackled the problem of integrating structured knowledge (e.g., theoretical or simulated insights) with data-driven neural networks by developing SKINNs, a unified framework that embeds differentiable constraints, resulting in improved out-of-sample valuation and hedging performance in financial applications, with enhanced stability in parameter recovery.
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.