Under a symmetric random walk, a static limit order that converts to a market order at the end has zero expected cost relative to immediate execution, for every limit price.
Markov , title On the design of sell-side limit and market order tactics , journal Journal of Trading volume 7 number 3 ( year 2012 ), pages 29--39
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Random walk model from the point of view of algorithmic trading
Under a symmetric random walk, a static limit order that converts to a market order at the end has zero expected cost relative to immediate execution, for every limit price.