A Mean-Field Game of Market-Making against Strategic Traders

IF 1.4 4区经济学 Q3 BUSINESS, FINANCE

SIAM Journal on Financial Mathematics Pub Date : 2023-10-18 DOI:10.1137/22m1486492

Bastien Baldacci, Philippe Bergault, Dylan Possamaï

引用次数: 0

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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对策略交易者做市的平均场博弈

我们设计了一个做市模型(la Avellaneda和Stoikov [Quant. Finance, 8 (2008)， pp. 217-224])，在这个模型中，市场接受者采取战略行动，从某种意义上说，他们根据外生交易信号设计交易策略。做市商根据市场接受者的平均行为选择报价，并通过平均场相互作用建模。在HJB-Fokker-Planck耦合系统的分辨率下，我们导出了做市商和代表性市场接受者的最优控制。这种方法足够灵活，可以将市场参与者的不同行为结合起来，并考虑到他们的策略对价格过程的影响。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Financial Mathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.