论文标题
带有信号的最佳清算：通用传播案例
Optimal Liquidation with Signals: the General Propagator Case
论文作者
论文摘要
我们考虑了一类最佳清算问题，在这些问题中，代理商的交易造成了瞬态价格影响，由摩尔拉型传播器驱动以及临时价格影响。我们将这些问题提出为最小化收入风险功能，在该功能中，代理还利用可逐步可测量的价格预测信号的可用信息。通过使用无限的尺寸随机控制方法，我们用解决方案的解决方案来表征值函数，以实现自由边界的$ l^2 $可值的向后随机微分方程和运算符值的riccati方程。然后，我们将分析解决方案得出这些方程式，该方程为最佳交易策略提供了明确的表达。我们表明，我们的公式可以直接有效地实施，以实现大量的价格影响内核，例如幂律内核。
We consider a class of optimal liquidation problems where the agent's transactions create transient price impact driven by a Volterra-type propagator along with temporary price impact. We formulate these problems as minimization of a revenue-risk functionals, where the agent also exploits available information on a progressively measurable price predicting signal. By using an infinite dimensional stochastic control approach, we characterize the value function in terms of a solution to a free-boundary $L^2$-valued backward stochastic differential equation and an operator-valued Riccati equation. We then derive analytic solutions to these equations which yields an explicit expression for the optimal trading strategy. We show that our formulas can be implemented in a straightforward and efficient way for a large class of price impact kernels with possible singularities such as the power-law kernel.
