Mean-Field Games with Differing Beliefs for Algorithmic Trading

Philippe Casgrain and Sebastian Jaimungal

Papers from arXiv.org

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.

Date: 2018-10, Revised 2019-12
New Economics Papers: this item is included in nep-cmp, nep-gth and nep-mst
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Citations: View citations in EconPapers (5)

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