A Mean-Field Game of Market-Making against Strategic Traders
Bastien Baldacci, Philippe Bergault, Dylan Possamaï
Source abstract
Abstract. We design a market-making model à la Avellaneda and Stoikov [ Quant. Finance, 8 (2008), pp. 217–224] 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’ behavior, 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 behaviors for the market-takers and takes into account the impact of their strategies on the price process.
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