An FBSDE approach to market impact games with stochastic parameters

IF 1 2区数学 Q3 STATISTICS & PROBABILITY

Probability Uncertainty and Quantitative Risk Pub Date : 2019-12-19 DOI:10.3934/puqr.2021012

Samuel Drapeau, Peng Luo, A. Schied, Dewen Xiong

引用次数: 7

Abstract

In this study, we have analyzed a market impact game between n risk-averse agents who compete for liquidity in a market impact model with a permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic differential equations (FBSDEs). Our second main result provides conditions under which this system of FBSDEs has a unique solution, resulting in a unique Nash equilibrium.

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随机参数下市场冲击博弈的FBSDE方法

在本研究中，我们分析了在具有永久价格影响和额外滑动的市场影响模型中，n个风险厌恶者之间争夺流动性的市场影响博弈。大多数市场参数，包括波动性和漂移，是允许随机变化的。我们的第一个主要结果将纳什均衡描述为一个完全耦合的前向后随机微分方程(FBSDEs)系统。我们的第二个主要结果提供了该FBSDEs系统具有唯一解的条件，从而产生唯一纳什均衡。

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

Probability Uncertainty and Quantitative Risk STATISTICS & PROBABILITY-

CiteScore

1.60

自引率

13.30%

发文量

审稿时长

12 weeks

期刊介绍： Probability, Uncertainty and Quantitative Risk (PUQR) is a quarterly academic journal under the supervision of the Ministry of Education of the People's Republic of China and hosted by Shandong University, which is open to the public at home and abroad (ISSN 2095-9672; CN 37-1505/O1). Probability, Uncertainty and Quantitative Risk (PUQR) mainly reports on the major developments in modern probability theory, covering stochastic analysis and statistics, stochastic processes, dynamical analysis and control theory, and their applications in the fields of finance, economics, biology, and computer science. The journal is currently indexed in ESCI, Scopus, Mathematical Reviews, zbMATH Open and other databases.