Switching investments

We present a simple online two-way trading algorithm that exploits fluctuations in the unit price of an asset. Rather than analysing worst-case performance under some assumptions, we prove a novel, unconditional performance bound that is parameterised either by the actual dynamics of the price of the asset, or by a simplifying model thereof. The algorithm processes T prices in O(T^2) time and O(T) space, but if the employed prior density is exponential, the time requirement reduces to O(T). The result translates to the prediction with expert advice framework, and has applications in data compression and hypothesis testing.