Bayesian Adaptive Trading with a Daily Cycle

Standard models of algorithmic trading neglect the presence of a daily cycle. We construct a model in which the trader uses information from observations of price evolution during the day to continuously update his estimate of other traders' target sizes and directions. He uses this information to determine an optimal trade schedule to minimize total expected cost of trading, subject to sign constraints (never buy as part of a sell program). We argue that although these strategies are determined using very simple dynamic reasoning—at each moment they assume that current conditions will last until the end of trading—they are in fact the globally optimal strategies as would be determined by dynamic programming.