Universal switching portfolios under transaction costs

In this paper, we consider online (sequential) portfolio selection in a competitive algorithm framework under transaction costs. We construct a sequential algorithm for portfolio selection that asymptotically achieves the wealth of the best piecewise constant rebalanced portfolio tuned to the underlying individual sequence of price relative vectors where we pay a fixed percent commission for each transaction. Without knowledge of the investment duration, the algorithm can perform as well as the best investment algorithm that can choose both the partitioning of the sequence of the price relative vectors as well as the best constant rebalanced portfolio within each segment based on knowledge of the sequence of price relative vectors in advance. We use a transition diagram similar to that in [1] to compete with an exponential number of switching investment strategies, using only linear complexity in the data length for combination.