Optimal solutions for the online time series search and one-way trading problem with interrelated prices and a profit function

We consider the online problems of time series search and one-way trading with interrelated prices. We derive two algorithms PUND and PDIV which extend the solutions found in literature with profit functions, derive the competitive ratio and prove optimality. For the new as well as for the established online algorithms, we give a numerical example. For the time series search problem with interrelated prices, we present another algorithm UND∗. This algorithm has constant time complexity and an explicit formula for the competitive ratio and selected period to sell. The current solution in literature has linear time complexity and no such explicit formulas.