Universal portfolio algorithms in realistic-outcome markets

Universal portfolio algorithms find investment strategies competitive against any CRP (constant rebalanced portfolio) for each and every market sequence. This work studies the problem of competitiveness over a subset of realistic, non-pathological, market sequences observed in many settings, e.g., high-frequency trading. Competitive investment in this setting will be shown to be more an extension of the easier universal 0-1 loss problem than of universal gambling (or coding). Analysis of realism-agnostic investment algorithms will show that they perform much better on in-hindsight realistic sequences than previously demonstrated. We suggest that this implies that the study of realistic universal portfolio algorithms must involve a comparison to a stronger adversary than the CRP adversary: an adversary that rebalances a portfolio often enough to avoid pathological sequences, but not so frequently that transaction costs dominate.