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In this short note, we study an optimization problem of expectedimplementation shortfall (IS) cost under general shaped market impactfunctions. In particular, we find that an optimal strategy is a VWAP (volumeweighted average price) execution strategy when the market model is aBlack-Scholes type with stochastic clock and market trading volume is large.

Optimality of VWAP Execution Strategies under General Shaped Market Impact Functions