🤖 AI Summary
This paper addresses the optimal liquidation problem under progressively measurable price prediction signals, incorporating both instantaneous and Volterra-type transient price impact—including singular power-law kernels. We propose the first framework jointly modeling predictive signals and the Volterra propagator, and solve it via infinite-dimensional stochastic control, yielding explicit analytical solutions: a free-boundary backward stochastic differential equation (BSDE) and an operator-valued Riccati equation. Our theoretical contributions are threefold: (i) we establish, for the first time, existence and uniqueness of the optimal strategy under signal-driven liquidation with singular Volterra kernels; (ii) we derive a closed-form expression for the optimal trading rate; and (iii) the resulting algorithm is computationally efficient and applicable to a broad class of price impact kernels. These results provide a rigorous mathematical foundation and practical execution strategies for high-frequency trading and algorithmic order execution.
📝 Abstract
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 maximization 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 ‐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.
