2024/11/16 by Yan Dolinsky, Dolinsky, Yan
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Economics and business #Fault Detection and Control Systems #Machine Learning and Algorithms #Mathematical Finance (q-fin.MF)
paper · pdf · doi:10.48550/arxiv.2411.10726
openalex publication_date 2024/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study an optimal execution problem in the infinite horizon setup. Our financial market is given by the Black-Scholes model with a linear price impact. The main novelty of the current note is that we study the constrained case where the number of shares and the selling rate are non-negative processes. For this case we give a complete characterization of the value and the optimal control via a solution of a non-linear ordinary differential equation (ODE). Furthermore, we provide an example where the non-linear ODE can be solved explicitly. Our approach is purely probabilistic.