Mean field game of controls and an application to trade crowding

By Pierre Cardaliaguet, Charles-Albert Lehalle. 2016

270 citations recorded by the source corpus.

In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a mean field game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader facing a “background noise” (or “mean field”). In standard frameworks, the interactions between the large trader and the price are a temporary and a permanent market impact terms, the latter influencing the public price. In this paper the trader faces the uncertainty of fair price changes too but not only. He also has to deal with price changes generated by other similar market participants, impacting the prices permanently too, and acting strategically. Our MFG formulation of this problem belongs to the class of “extended MFG”, we hence provide generic results to address these “MFG of controls”, before solving the one generated by the cost function of optimal trading. We provide a closed form formula of its solution, and address the case of “heterogenous preferences” (when each participant has a different risk aversion). Last but not least we give conditions under which participants do not need to instantaneously know the state of the whole system, but can “learn” it day after day, observing others’ behaviors.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/a9db890291792ac765763a8cd2ed27a60a56fb69

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

Citations in the corpus

Mean field and n‐agent games for optimal investment under relative performance criteria (2017, background): “While randomizing types is a standard technique in static games with a continuum of agents, the idea has scarcely appeared in the (dynamic) MFG literature; to the best of our knowledge, it has appeared only in Cardaliaguet and Lehalle (2016).”
Some remarks on mean field games (2018, background): “See the example studied in [23] for example.”
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games (2019, methodology): “, Carleo and Troyer (2017); Gao and Duan (2017); Han et al. (2018); Zhang et al. (2018b); Han et al. (2019)). Considering the astonishing performance of the DNN, we shall leverage it to help identify the Nash equilibrium through solving high-dimensional coupled HJB equations. To achieve this, we des”