A Posteriori Multistage Optimal Trading under Transaction Costs and a Diversification Constraint

This article presents a simple method for a posteriori (historical) multivariate, multistage optimal trading under transaction costs and a diversification constraint. Starting from a given amount of money in some currency, the authors analyze the stage-wise optimal allocation over a time horizon with potential investments in multiple currencies and various assets. Three variants are discussed: unconstrained trading frequency, a fixed number of total admissible trades, and waiting 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.