跳至正文
返回文库全部文档

具有潜在信息与市场冲击的均值场交易

文章 arXiv papers · 作者: Philippe Casgrain et al.
阅读原文

总结

本文对异质主体之间的算法交易建模，这些主体无法直接观察潜在市场状态。主体通过滤波估计这些状态，并进行最优执行或统计套利交易。其行为会产生永久和暂时的价格冲击，使这一设定成为参与者相互作用的大型随机博弈。

作者研究包含多个主体子群体的均值场极限，并运用凸分析，通过向量值前向后向随机微分方程刻画均衡。作者证明解存在且唯一，推导出闭式解，刻画主体的均衡行为，并证明该均值场策略可以近似有限主体博弈中的均衡。模拟示例展示了这一策略。所提供的文本未说明市场校准、实证表现或实际执行约束，因此这些结果属于理论和模拟结果，并非实盘交易盈利的证据。

核心观点

  • 主体在选择交易行为之前，会通过滤波估计潜在市场状态。
  • 模型纳入了从事交易执行或统计套利的异质交易者。
  • 随机博弈中的交易会造成永久和暂时的价格冲击。
  • 均值场极限导出一个由前向后向随机系统刻画的均衡。
  • 研究证明该均衡可以近似有限主体情形下的纳什均衡，并通过模拟加以说明。

标签

交易执行套利市场微观结构统计学
全文
# Mean Field Games with Partial Information for Algorithmic Trading


# Mean Field Games with Partial Information for Algorithmic Trading









Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where all agents filter the latent states of the world, and their trading actions have permanent and temporary price impact. This leads to a large stochastic game with heterogeneous agents. We solve the stochastic game by investigating its mean-field game (MFG) limit, with sub-populations of heterogeneous agents, and, using a convex analysis approach, we show that the solution is characterized by a vector-valued forward-backward stochastic differential equation (FBSDE). We demonstrate that the FBSDE admits a unique solution, obtain it in closed-form, and characterize the optimal behaviour of the agents in the MFG equilibrium. Moreover, we prove the MFG equilibrium provides an $ε$-Nash equilibrium for the finite player game. We conclude by illustrating the behaviour of agents using the optimal MFG strategy through simulated examples.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。