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This paper presents a simple method for a posteriori (historical)multi-variate multi-stage optimal trading under transaction costs and adiversification constraint. Starting from a given amount of money in somecurrency, we analyze the stage-wise optimal allocation over a time horizon withpotential investments in multiple currencies and various assets. Three variantsare discussed, including unconstrained trading frequency, a fixed number oftotal admissable trades, and the waiting of a specific time-period after everyexecuted trade until the next trade. The developed methods are based onefficient graph generation and consequent graph search, and are evaluatedquantitatively on real-world data. The fundamental motivation of this work ispreparatory labeling of financial time-series data for supervised machinelearning.

A posteriori multi-stage optimal trading under transaction costs and a diversification constraint