Artificial Intelligence and Systemic Risk: A Unified Model of Performative Prediction, Algorithmic Herding, and Cognitive Dependency in Financial Markets

We develop a unified model in which AI adoption in financial markets generates systemic risk through three mutually reinforcing channels: performative prediction, algorithmic herding, and cognitive dependency. Within an extended rational expectations framework with endogenous adoption, we derive an equilibrium systemic risk coupling r(φ) = φρβ/λ'(φ), where φ is the AI adoption share, ρ the algorithmic signal correlation, β the performative feedback intensity, and λ'(φ) the endogenous effective price impact. Because λ'(φ) is decreasing in φ, the coupling is convex in adoption, implying that the systemic risk multiplier M = (1 - r)-1 grows superlinearly as AI penetration increases. The model is developed in three layers. First, endogenous fragility: market depth is decreasing and convex in AI adoption. Second, embedding the convex coupling within a supermodular adoption game produces a saddle-node bifurcation into an algorithmic monoculture. Third, cognitive dependency as an endogenous state variable yields an impossibility theorem (hysteresis requires dynamics beyond static frameworks) and a channel necessity theorem (each channel is individually necessary). Empirical validation uses the complete universe of SEC Form 13F filings (99.5 million holdings, 10,957 institutional managers, 2013--2024) with a Bartik shift-share instrument (first-stage F = 22.7). The model implies tail-loss amplification of 18--54%, economically significant relative to Basel III countercyclical buffers.