Paper: arXiv 2601.09872

Authors: Eunjung Noh

Abstract

Classical Kyle-type models of informed trading typically treat noise trader demand as purely exogenous. In reality, many market participants react to price movements and news, generating feedback effects that can significantly alter market dynamics. This paper develops a continuous-time Kyle framework in which two types of price-responsive traders (momentum and contrarian traders) adjust their demand in response to price signals. This extension yields a finite-dimensional Kalman filter for price discovery and leads to a forward-backward Riccati system characterizing equilibrium. We show that when feedback is weak, equilibrium exists and is unique as a smooth perturbation of the classical Kyle solution, allowing us to derive explicit comparative statics for insider profits and price informativeness. For stronger feedback, the model generates rich dynamics, including potential multiplicity of equilibria and amplification effects. Our framework thus bridges the gap between purely exogenous noise and more realistic, behaviorally motivated trading.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical extension of the continuous-time Kyle model by introducing endogenous momentum and contrarian traders within a finite-dimensional Kalman-Bucy filtering framework. While highly sophisticated and theoretically novel in its derivation of forward-backward Riccati systems and equilibrium stability breakdown mechanisms, it is purely theoretical and completely lacks empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Incorporate price-responsive traders (momentum & contrarian) into continuous-time Kyle model"] --> B["Framework Inputs: Informed insider signal & feedback-driven noise trader demand"]
    B --> C["Formulate Continuous-Time Kyle Framework"]
    C --> D["Apply Finite-Dimensional Kalman Filter for Price Discovery"]
    D --> E["Derive Forward-Backward Riccati System for Equilibrium"]
    E --> F["Weak Feedback Outcome: Unique equilibrium, explicit comparative statics for profits & informativeness"]
    E --> G["Strong Feedback Outcome: Equilibrium multiplicity & market amplification effects"]

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1 of 82 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.