英文标题：
《Endogenous Formation of Limit Order Books: Dynamics Between Trades》
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作者：
Roman Gayduk and Sergey Nadtochiy
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最新提交年份：
2017
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英文摘要：
In this work, we present a continuous-time large-population game for modeling market microstructure betweentwo consecutive trades. The proposed modeling framework is inspired by our previous work [23]. In this framework, the Limit Order Book (LOB) arises as an outcome of an equilibrium between multiple agents who have different beliefs about the future demand for the asset. The agents\' beliefs may change according to the information they observe, triggering changes in their behavior. We present an example illustrating how the proposed models can be used to quantify the consequences of changes in relevant information signals. If these signals, themselves, depend on the LOB, then, our approach allows one to model the \"indirect\" market impact (as opposed to the \"direct\" impact that a market order makes on the LOB, by eliminating certain limit orders). On the mathematical side, we formulate the proposed modeling framework as a continuum-player control-stopping game. We manage to split the equilibrium problem into two parts. The first one is described by a two-dimensional system of Reflected Backward Stochastic Differential Equations (RBSDEs), whose solution components reflect against each other. The second one leads to an infinite-dimensional fixed-point problem for a discontinuous mapping. Both problems are non-standard, and we prove the existence of their solutions in the paper.
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中文摘要：
在这项工作中，我们提出了一个连续时间大人口博弈模型，用于模拟两个连续交易之间的市场微观结构。拟议的建模框架受到我们之前工作的启发【23】。在此框架中，限额订单簿（LOB）是多个对资产未来需求有不同信念的代理之间平衡的结果。代理人的信念可能会根据他们观察到的信息而改变，从而引发他们行为的改变。我们给出了一个示例，说明如何使用所提出的模型来量化相关信息信号变化的后果。如果这些信号本身取决于LOB，那么我们的方法允许我们对“间接”市场影响进行建模（与市场订单通过取消某些限额订单对LOB产生的“直接”影响相反）。在数学方面，我们将所提出的建模框架描述为一个连续的玩家控制-停止博弈。我们设法把平衡问题分成两部分。第一种是由二维反射倒向随机微分方程（RBSDE）系统描述的，其解分量相互反射。第二个问题导致不连续映射的无穷维不动点问题。这两个问题都是非标准的，本文证明了它们解的存在性。
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分类信息：

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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