Algorithmic Trading with Partial Information: A Mean Field Game Analysis

Financial markets are often driven by latent factors. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform statistical arbitrage in such latent environments, and the... [ view full abstract ]

Financial markets are often driven by latent factors. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform statistical arbitrage in such latent environments, and the trading actions of all agents have permanent and temporary impact. We solve the stochastic game by investigating its mean-field game limit and, using a novel convex analysis approach, we show that the solution is characterized by a vector-valued FBSDE. We demonstrate that the FBSDE admits a unique solution, and obtain it in closed-form. Moreover, we prove that the MFG equilibrium provides an $\epsilon$-Nash equilibrium for the finite game.