Optimal Execution and Price Manipulations in Time-varying Limit Order Books

This paper focuses on an extension of the limit order book (LOB) model with general shape introduced by Alfonsi, Fruth and Schied ((2010). Optimal execution strategies in limit order books with general shape functions. <italic>Quantitative Finance</italic>, <italic>10</italic>(2), 143-157). Here, the additional feature allows a time-varying LOB depth. We solve the optimal execution problem in this framework for both discrete and continuous time strategies. This gives in particular sufficient conditions to exclude price manipulations in the sense of Huberman and Stanzl ((2004). Price manipulation and quasi-arbitrage. <italic>Econometrica</italic>, <italic>72</italic>(4), 1247-1275) or transaction-triggered price manipulations (see Alfonsi, A., Schied, A., & Slynko, A. (2012). Order book resilience, prince manipulation, and the positive portfolio problem. <italic>SIAM Journal of Financial Mathematics, 3,</italic> 511-533.). These conditions give interesting qualitative insights on how market makers may create or not price manipulations.