Switching investments

We present two simple online two-way trading algorithms that exploit fluctuations in the unit price of an asset. Rather than analysing worst-case performance under some assumptions, we prove novel, unconditional performance bounds that are parameterised by a regularisation of the actual dynamics of the price of the asset. The algorithm processes T prices in O(T2) time and O(T) space, but if the employed prior density is exponential, the time requirement reduces to O(T). The algorithm does the same in O(T) time and O(1) space, for any prior; its bound is slightly stronger than the bound for but only applies to a single regularisation that is determined by the algorithm. The result translates to the prediction with expert advice framework, and has applications in data compression and hypothesis testing.