{"ID":2829325,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.12708","arxiv_id":"2512.12708","title":"Multi-Trajectory Physics-Informed Neural Networks for HJB Equations with Hard-Zero Terminal Inventory: Optimal Execution on Synthetic \u0026 SPY Data","abstract":"We study optimal trade execution with a hard-zero terminal inventory constraint, modeled via Hamilton-Jacobi-Bellman (HJB) equations. Vanilla PINNs often under-enforce this constraint and produce unstable controls. We propose a Multi-Trajectory PINN (MT-PINN) that adds a rollout-based trajectory loss and propagates a terminal penalty on terminal inventory via backpropagation-through-time, directly enforcing zero terminal inventory. A lightweight lambda-curriculum is adopted to stabilize training as the state expands from a risk-neutral reduced HJB to a risk-averse HJB. On the Gatheral-Schied single-asset model, MT-PINN aligns closely with their derived closed-form solutions and concentrates terminal inventory tightly around zero while reducing errors along optimal paths. We apply MT-PINNs on SPY intraday data, matching TWAP when risk-neutral, and achieving lower exposure and competitive costs, especially in falling windows, for higher risk-aversion.","short_abstract":"We study optimal trade execution with a hard-zero terminal inventory constraint, modeled via Hamilton-Jacobi-Bellman (HJB) equations. Vanilla PINNs often under-enforce this constraint and produce unstable controls. We propose a Multi-Trajectory PINN (MT-PINN) that adds a rollout-based trajectory loss and propagates a t...","url_abs":"https://arxiv.org/abs/2512.12708","url_pdf":"https://arxiv.org/pdf/2512.12708v1","authors":"[\"Anthime Valin\"]","published":"2025-12-14T14:20:58Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.OC\"]","methods":"[\"Large Language Model\"]","has_code":false}