A mean-field game of market-making against strategic traders

Bastien Baldacci, Philippe Bergault () and Dylan Possamaï
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Philippe Bergault: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: We design a market-making model \`a la Avellaneda-Stoikov in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers' behaviour, modelled through a mean-field interaction. We derive, up to the resolution of a coupled HJB--Fokker--Planck system, the optimal controls of the market-maker and the representative market-taker. This approach is flexible enough to incorporate different behaviours for the market-takers and takes into account the impact of their strategies on the price process.

Date: 2022-03-24
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Published in SIAM Journal on Financial Mathematics, 2022, 14 (4), pp.1080-1112. ⟨10.1137/22M1486492⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03941548

DOI: 10.1137/22M1486492

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