Mean-Field Games with Differing Beliefs for Algorithmic Trading

TL;DR

This paper models how heterogeneous agents with differing beliefs interact in algorithmic trading, analyzing the mean-field game limit, and demonstrating that disagreement can increase market volatility and trading activity.

Contribution

It introduces a novel mean-field game framework for agents with differing beliefs, including a new solution approach and an algorithm for computing equilibria.

Findings

Disagreement among agents can lead to increased market volatility.

The proposed algorithm effectively computes equilibria in complex trading scenarios.

Increasing disagreement correlates with higher trading activity.

Abstract

Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for the permanent impact they have on prices. This leads to a large stochastic game, where each agents' performance criteria are computed under a different probability measure. We analyse the mean-field game (MFG) limit of the stochastic game and show that the Nash equilibrium is given by the solution to a non-standard vector-valued forward-backward stochastic differential equation. Under some mild assumptions, we construct the solution in terms of expectations of the filtered states. Furthermore, we prove the MFG strategy forms an $\epsilon$-Nash equilibrium for the finite player game. Lastly, we present a least-squares Monte Carlo based algorithm for computing the equilibria and show through simulations that increasing disagreement may increase price volatility and trading activity.