The statistical adversary allows optimal money-making trading strategies

The distributional approach and competitive analysis have traditionally been used for the design and analysis of online algorithms. The former assumes a specific distribution of inputs, while the latter assumes inputs are chosen by an unrestricted adversary. This paper employs the statistical adversary (recently proposed by Raghavan) to analyze and design on-line algorithms for two-way cumncy trading. By statistical adversary, we mean an adversary that generates worst case input sequences, where each sequence must satisfy certain general statistical properties. The on-line algorithms presented in this paper have some very attractive properties. For instance, the algorithms are money-making. Although previous on-line algorithms are competitive, they can lose money even when the optimal off-line algorithm makes money. Against a weak statistical adversary, our methods yield an algorithm that outperforms the optimal off-line “buy-and-hold” strategy. Furthermore, it is guaranteed to make a substantial profit when it is known that the market is active and stable. In fact, our algorithm even makes money when the market exhibits a slightly unfavorable trend.