Abstract:This paper develops a unified explicit solution theory for optimal execution through sequential limit-order placement in a limit order book. Rather than controlling only the trading speed of a metaorder, we determine how individual limit orders should be quoted over time. The model incorporates signal-dependent drift, price impact, inventory risk, and execution risk, with fills modeled by point processes whose intensities depend on the submitted quotes. We formulate four execution criteria: expected terminal wealth, expected terminal wealth with running inventory penalty, CARA utility of terminal wealth, and CARA utility with running inventory penalty. For general price-impact and inventory-penalty functions, we derive the corresponding HJB equations and show that all four problems reduce to a triangular finite-dimensional structure which can be solved explicitly, leading to fully explicit value functions and optimal quotes across all cases. We also prove well-posedness, admissibility, and verification results. The explicit formulas reveal connections between quoting strategies under different criteria, support long-horizon asymptotic analysis, and show numerically that signal-dependent drift can substantially affect optimal execution.
| Comments: | 48 pages, 11 figures |
| Subjects: | Trading and Market Microstructure (q-fin.TR); Optimization and Control (math.OC); Mathematical Finance (q-fin.MF) |
| MSC classes: | 91G80, 93E20, 49N90 |
| Cite as: | arXiv:2605.24242 [q-fin.TR] |
| (or arXiv:2605.24242v1 [q-fin.TR] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24242 arXiv-issued DOI via DataCite (pending registration) |
From: Fenghui Yu [view email]
[v1]
Fri, 22 May 2026 21:36:45 UTC (475 KB)
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