Robust time to buy and sell stock

This paper focuses on the robust version of the classical algorithmic problem of finding the best time to buy and sell stock. We consider its variants with different transaction limits, as well as other modifications like transaction fee or cooldown. We reduce each classical problem to its robust version, thereby obtaining lower bounds on the time complexity of all potential solutions. We extensively test all developed methods on random and adversarial data to ensure correctness and evaluate performance. We propose efficient methods for the robust counterparts of almost all problems. We also discuss suboptimal polynomial method based on dynamic programming techniques for the limited number of transactions. Developed methods are valuable in the practical applications of stock trading to obtain a minimum regret solution and evaluate the regret of an existing solution. We expect these applications of dynamic programming techniques to robust optimization problems to be relatively easy to extend and generalize for similar issues in combinatorial optimization.