Mean Field Trading with Latent Information and Market Impact

Summary

This paper models algorithmic trading among heterogeneous agents who cannot directly observe latent market states. Agents estimate those states through filtering and trade for optimal execution or statistical arbitrage. Their actions create both permanent and temporary price impact, making the setting a large stochastic game with interacting participants.

The authors study a mean-field limit with multiple agent subpopulations and use convex analysis to characterize equilibrium through a vector-valued forward-backward stochastic differential equation. They establish a unique solution, derive it in closed form, characterize the agents’ equilibrium behavior, and prove that this mean-field strategy approximates an equilibrium in the finite-agent game. Simulated examples illustrate the strategy. The supplied text does not specify market calibration, empirical performance, or practical execution constraints, so the results are theoretical and simulation-based rather than evidence of live trading profitability.

Key ideas

• Agents filter latent market states before choosing trading actions.
• The model includes heterogeneous traders pursuing execution or statistical arbitrage.
• Trading creates permanent and temporary price impact in the stochastic game.
• A mean-field limit yields an equilibrium characterized by a forward-backward stochastic system.
• The equilibrium is shown to approximate a Nash equilibrium for the finite-agent setting and is illustrated with simulations.

Tags

# Mean Field Games with Partial Information for Algorithmic Trading


# Mean Field Games with Partial Information for Algorithmic Trading









Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where all agents filter the latent states of the world, and their trading actions have permanent and temporary price impact. This leads to a large stochastic game with heterogeneous agents. We solve the stochastic game by investigating its mean-field game (MFG) limit, with sub-populations of heterogeneous agents, and, using a convex analysis approach, we show that the solution is characterized by a vector-valued forward-backward stochastic differential equation (FBSDE). We demonstrate that the FBSDE admits a unique solution, obtain it in closed-form, and characterize the optimal behaviour of the agents in the MFG equilibrium. Moreover, we prove the MFG equilibrium provides an $ε$-Nash equilibrium for the finite player game. We conclude by illustrating the behaviour of agents using the optimal MFG strategy through simulated examples.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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