论文标题
差异riccati方程和应用于信号的算法交易的应用
Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals
论文作者
论文摘要
我们研究具有无限基质系数的差异性Riccati方程（DRE），这是在广泛的实际问题中产生的。我们表明，DRE解决了相关的控制问题，这是提供解决方案的存在和独特性的关键。作为一个应用程序，我们解决了两个算法交易问题，其中代理采用恒定的绝对风险规避（CARA）公用事业功能，以及最佳策略使用信号和过去对价格的观察来提高其性能。首先，我们在非处方市场中得出了一个多资产市场制定策略，市销商使用外部交易场所来对冲风险。其次，我们得出了一种最佳交易策略，该策略使用价格和信号来了解资产价格的漂移。
We study a differential Riccati equation (DRE) with indefinite matrix coefficients, which arises in a wide class of practical problems. We show that the DRE solves an associated control problem, which is key to provide existence and uniqueness of a solution. As an application, we solve two algorithmic trading problems in which the agent adopts a constant absolute risk-aversion (CARA) utility function, and where the optimal strategies use signals and past observations of prices to improve their performance. First, we derive a multi-asset market making strategy in over-the-counter markets, where the market maker uses an external trading venue to hedge risk. Second, we derive an optimal trading strategy that uses prices and signals to learn the drift in the asset prices.
