ON AN UPPER GAIN BOUND FOR STRATEGIES WITH CONSTANT AND PROPORTIONAL NUMBER OF ASSETS TRADED

We introduce general formulas for the upper bound of gain obtained from any finite-time trading strategy in discrete and continuous time models. We consider strategies with constant number of assets traded and strategies with proportional number of assets traded. Unfortunately, the estimates obtained in the discrete case become trivial in the continuous case, hence we introduce transaction costs. This leads to the interesting estimates in terms of the so called truncated variation of the price series. We apply the obtained estimates in specific cases of financial time series.