英文标题：
《Mean Field Games with Partial Information for Algorithmic Trading》
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作者：
Philippe Casgrain, Sebastian Jaimungal
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最新提交年份：
2019
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英文摘要：
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 $\\epsilon$-Nash equilibrium for the finite player game. We conclude by illustrating the behaviour of agents using the optimal MFG strategy through simulated examples.
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中文摘要：
金融市场往往由交易员无法观察到的潜在因素驱动。在这里，我们讨论了一个算法交易问题，其中的异构代理集合旨在执行最佳执行或统计套利，其中所有代理过滤世界的潜在状态，并且其交易行为具有永久和临时的价格影响。这导致了一个具有异构代理的大型随机博弈。我们通过研究随机对策的平均场对策（MFG）极限来求解该随机对策，并利用凸分析方法证明了该解的特征是一个向量值正倒向随机微分方程（FBSDE）。我们证明了FBSDE允许一个唯一的解，以闭合形式获得它，并描述了MFG平衡中代理的最优行为。此外，我们证明了MFG均衡为有限人博弈提供了$\\ε$-纳什均衡。最后，我们通过模拟示例说明了使用最优制造策略的代理行为。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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