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Mean field game of controls and an application to trade crowding

Cardaliaguet, Pierre ; Lehalle, Charles-Albert

Mathematics and financial economics, 2018-06, Vol.12 (3), p.335-363 [Periódico revisado por pares]

Berlin/Heidelberg: Springer Berlin Heidelberg

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Título:
Mean field game of controls and an application to trade crowding
Autor: Cardaliaguet, Pierre ; Lehalle, Charles-Albert
Assuntos: Applications of Mathematics ; Background noise ; Bankruptcy ; Crowding ; Economic models ; Economic Theory/Quantitative Economics/Mathematical Methods ; Economics ; Finance ; Insurance ; Macroeconomics/Monetary Economics//Financial Economics ; Management ; Markets ; Mathematics ; Mathematics and Statistics ; Noise ; Prices ; Pricing ; Quantitative Finance ; Risk ; Statistics for Business ; Trading ; Uncertainty
É parte de: Mathematics and financial economics, 2018-06, Vol.12 (3), p.335-363
Descrição: 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.
Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
Idioma: Inglês

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Mean field game of controls and an application to trade crowding

Cardaliaguet, Pierre ; Lehalle, Charles-Albert

Berlin/Heidelberg: Springer Berlin Heidelberg

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