论文标题
算法交易中儿童订单放置的随机LQR模型
A Stochastic LQR Model for Child Order Placement in Algorithmic Trading
论文作者
论文摘要
现代算法交易（“ ALGO”）允许机构投资者和商人以全自动或低接触方式清算或建立大型安全职位。大多数现有的学术或工业算法都集中在如何在给定时间范围内将大父订单“切成”较小的子订单。很少有模型严格解决这些儿童订单的实际位置。取而代之的是，位置主要是通过经验信号和启发式决策过程组合来完成的。由于所有固有的复杂性，例如由于多个场所，限制顺序书籍的动态，点亮与深色流动性，不同的交易式和不同的交易，会议和规则，因此，独立，现实且功能齐全的儿童订单放置（COP）模型可能永远不存在。在本文中，我们提出了一个简化主义COP模型，该模型仅专注于放置被动限制顺序与使用积极的外卖订单进行狙击之间的相互作用。动态编程模型采用随机线性界面调节器（LQR）的形式，并允许在向后钟形方程下进行封闭形式的解决方案。详细探讨的是模型假设和一般设置，状态和控制变量的选择以及成本函数以及封闭形式解决方案的推导。
Modern Algorithmic Trading ("Algo") allows institutional investors and traders to liquidate or establish big security positions in a fully automated or low-touch manner. Most existing academic or industrial Algos focus on how to "slice" a big parent order into smaller child orders over a given time horizon. Few models rigorously tackle the actual placement of these child orders. Instead, placement is mostly done with a combination of empirical signals and heuristic decision processes. A self-contained, realistic, and fully functional Child Order Placement (COP) model may never exist due to all the inherent complexities, e.g., fragmentation due to multiple venues, dynamics of limit order books, lit vs. dark liquidity, different trading sessions and rules. In this paper, we propose a reductionism COP model that focuses exclusively on the interplay between placing passive limit orders and sniping using aggressive takeout orders. The dynamic programming model assumes the form of a stochastic linear-quadratic regulator (LQR) and allows closed-form solutions under the backward Bellman equations. Explored in detail are model assumptions and general settings, the choice of state and control variables and the cost functions, and the derivation of the closed-form solutions.
