Differential Beliefs in Financial Markets Under Information Constraints: A Modeling Perspective

TL;DR

This paper uses advanced stochastic differential equations and optimization tools to analyze how partial information and differential beliefs influence market efficiency, bias reduction, and opinion aggregation in financial markets.

Contribution

It introduces a modeling framework based on McKean-Vlasov SDEs to study market behavior under information constraints, providing theoretical insights and practical simulations.

Findings

Market prices converge to true prices with increasing information.

Biases shrink as information flow increases.

Optimal opinion aggregation can yield positive alpha for traders.

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.