Optimal solutions for online conversion problems with interrelated prices

We consider various online conversion problems with interrelated prices. The first variant is the online time series search problem with unknown bounds on the relative price change factors. We design the optimal online algorithm IPN to solve this problem. We then consider the time series search with known bounds. Using the already established UND algorithm of Zhang et al. (J Comb Optim 23(2):159–166, 2012), we develop a new optimal online algorithm oUND which improves the experimental performance of the already existing optimal online algorithm for selected parameter constellations. We conduct a comparative experimental testing of UND and oUND and establish the parameter combinations for which one algorithm is better than the other. We then combine these two algorithms into a new one called cUND. This algorithm incorporates the strengths of UND and oUND and is also optimal online. Finally, we consider another variant, the general k -max search problem with interrelated prices, and also develop an optimal online algorithm.