2022/11/01 by Jaber, Eduardo Abi, Neuman, Eyal · 3 citations
#60H30 #91G80 #93E20 #FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Trading and Market Microstructure (q-fin.TR)
paper · doi:10.48550/arxiv.2211.00447
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 L2-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.