Mean Field Game Theory for Systems with Partial Observations and its Applications to Execution Problems in Finance

Peter Caines
McGill University

Partially observed mean field game (PO MFG) theory studies systems with a population of asymptotically negligible minor agents and, possibly, a major agent, where in the general case all minor agents partially observe their own and the major agent's state, and the major agent partially observes its own state. Subject to technical conditions, the existence of e-Nash equilibria may be established, together with the corresponding individual agents' (best response) control laws which depend upon information states generated by nonlinear filters associated to each agent.

The optimal execution problem in financial markets may be formulated in terms of a population of high frequency traders (minor agents) together with an institutional (major) investor, all of whom are (i) coupled through the mean field inherent in the market, and (ii) have partial observations on the their individual states and on the major agent's inventory. Furthermore, each agent is assumed to have a utility function reflecting the agents’ interest in maximizing their individual terminal wealth while avoiding both large execution prices and high trading rates. An application of PO MFG theory for linear stochastic systems with quadratic utility functions gives the best rate of trading for each agent to maximize its utility function in the e-Nash equilibrium sense.

Work with A.Kizilkale, N. Sen and D. Firoozi.

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