快慢投资者的 Stackelberg 交易策略
文章 arXiv papers · 作者: Rama Cont et al.
总结
本文对低频机构投资者与高频交易者之间的互动进行建模，二者的订单共同影响资产价格。交易速度更快的一方更频繁地观察价格预测信号，但面临定期的日终库存约束。他们的决策被表示为相互耦合的随机控制问题：先优化高频交易者的策略，再据此求解机构的策略。
作者通过求解弗雷德霍姆积分方程刻画多期 Stackelberg 均衡。在所得模型中，高频交易者在特定时期可能采取掠夺性或合作性行为，具体取决于订单流影响与预测信号之间的平衡。分析还发现，如果机构的策略考虑了高频交易者的订单流，机构收益会更高。这些是特定博弈模型下的理论结果；本文没有提供实证测试、校准，也没有证据表明这些策略在实盘市场中仍保持其性质。
核心观点
- 模型将低频机构和高频交易者视为会通过订单影响价格的策略参与者。
- 交易速度更快的一方更频繁地使用预测信号，并须满足定期库存约束。
- 机构的最优策略会考虑更快交易者根据市场信号调整的订单流。
- 根据预测信号和订单流的影响，均衡解允许出现掠夺性或合作性行为。
- 盈利能力方面的结果属于理论结论，取决于模型假设。
标签
全文
# Fast and Slow Optimal Trading with Exogenous Information # Fast and Slow Optimal Trading with Exogenous Information We consider a stochastic game between a slow institutional investor and a high-frequency trader who are trading a risky asset and their aggregated order-flow impacts the asset price. We model this system by means of two coupled stochastic control problems, in which the high-frequency trader exploits the available information on a price predicting signal more frequently, but is also subject to periodic "end of day" inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal signal-adaptive strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution to the game, which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is considerably more profitable when the order-flow of the high-frequency trader is taken into account in her trading strategy.
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