Paper: arXiv 2511.01486

Authors: Karen Grigorian, Robert Jarrow

Abstract

We apply the theory of McKean-Vlasov-type SDEs to study several problems related to market efficiency in the context of partial information and partially observable financial markets: (i) convergence of reduced-information market price processes to the true price process under an increasing information flow; (ii) a specific mechanism of shrinking biases under increasing information flows; (iii) optimal aggregation of expert opinions by a trader seeking a positive alpha. All these problems are studied by means of (conditional) McKean-Vlasov-type SDEs, Wasserstein barycenters, KL divergence and relevant tools from convex optimization, optimal control and nonlinear filtering. We supply the theoretical results in (i)-(iii) with concrete simulations demonstrating how the proposed models can be applied in practice to model financial markets under information constraints and the arbitrage-seeking behavior of traders with differential beliefs.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly sophisticated mathematical treatment of financial market efficiency and differential beliefs using McKean-Vlasov SDEs, Wasserstein barycenters, and nonlinear filtering. However, its empirical rigor is limited primarily to theoretical framework development and basic simulation studies, lacking validation against real-world market datasets.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Market Efficiency & Differential Beliefs Under Information Constraints] --> B[Input Data: Partially Observable Prices, Expert Opinions & Information Flows]
    B --> C[Methodology: McKean-Vlasov SDEs, Nonlinear Filtering & KL Divergence]
    C --> D[Computational Optimization: Wasserstein Barycenters & Optimal Control]
    D --> E[Key Findings: Convergence to True Price, Bias Shrinkage & Optimal Alpha Aggregation]