A continuous-time Kyle model with price-responsive traders

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.