  This paper presents a simple method for a posteriori (historical)
multi-variate multi-stage optimal trading under transaction costs and a
diversification constraint. Starting from a given amount of money in some
currency, we analyze the stage-wise optimal allocation over a time horizon with
potential investments in multiple currencies and various assets. Three variants
are discussed, including unconstrained trading frequency, a fixed number of
total admissable trades, and the waiting of a specific time-period after every
executed trade until the next trade. The developed methods are based on
efficient graph generation and consequent graph search, and are evaluated
quantitatively on real-world data. The fundamental motivation of this work is
preparatory labeling of financial time-series data for supervised machine
learning.
