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

• URL: http://arxiv.org/abs/2604.00987v1
• Date: Wed, 01 Apr 2026 14:51:08 GMT
• Title: Bridging Structured Knowledge and Data: A Unified Framework with Finance Applications
• Abstract summary: We develop a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function approximation.<n>SKINNs jointly estimate neural network parameters and economically meaningful structural parameters in a single optimization problem.<n>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.
• Score: 1.2805359127629214
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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