Title: Mean-Field Games with Differing Beliefs for Algorithmic Trading,
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 is computed under a
different probability measure. We analyse the mean-field game (MFG) limit of
the stochastic game and show that the Nash equilibria 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. 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 optimal control and
illustrate the results through simulation in market where agents disagree on
the model.