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 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 yield 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.

This is a joint work with Eduardo Abi-Jaber 

Bio

Eyal Neuman is a Senior Lecturer in mathematical finance and a member of the stochastic analysis research group at the Department of Mathematics, Imperial College London. His research interests are in the areas of probability, stochastic processes and mathematical finance. He is mainly working on interacting particle systems, stochastic partial differential equations and market microstructure. Previously he was a Visiting Assistant Professor at the University of Rochester, NY. Eyal received his PhD in stochastic processes from the Technion.