Robust one-way trading with limited number of transactions and heuristics for fixed transaction costs

A one-way trader has a certain amount of goods to trade over a finite period of time, but faces price uncertainties for which a probability distribution is unavailable. The problem becomes even more complicated with fixed transaction cost, which is very common in real world. Limiting the total number of transactions to control for transaction costs seems straightforward, but how to implement this effectively in real time with efficient algorithms backed by theoretical results is a big challenge and has not been well studied in the literature. Such one-way trading problem with limited number of transactions is formulated in a robust optimization framework. Theoretical analysis finds the optimal trading strategy with closed-form solution, identifies the worst price scenarios to help gain trading insights and spot trading opportunities, and shows that in the worst scenario, all of the optimal trades are of equal amount. On the practice side, a highly efficient heuristic to deal with fixed transaction costs is designed by choosing a proper limit on the number of transactions and merging trades on the fly, whose effectiveness and robustness are demonstrated by numerical experiments. The heuristic for selling employs a dynamic scheme with gradually increasing reservation price, in stark contrast to the static scheme with decreasing reservation price when the price distribution is known, which helps explain the robust performance of the proposed heuristic.