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Mean Field Game of Controls and An Application To Trade Crowding

Cardaliaguet, Pierre; Lehalle, Charles-Albert (2017), Mean Field Game of Controls and An Application To Trade Crowding, Mathematics and Financial Economics, p. 29. 10.1007/s11579-017-0206-z

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
Mathematics and Financial Economics
Publisher
Springer
Pages
29
Publication identifier
10.1007/s11579-017-0206-z
Metadata
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Author(s)
Cardaliaguet, Pierre
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Lehalle, Charles-Albert cc
Department of Mathematics [Imperial College London]
Abstract (EN)
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 in front of 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 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."
Subjects / Keywords
crowding; optimal liquidation; optimal trading; Mean field games; stochastic control
JEL
D53 - Financial Markets
G14 - Information and Market Efficiency; Event Studies; Insider Trading
C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games
C61 - Optimization Techniques; Programming Models; Dynamic Analysis

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