The upper bound of cumulative return of a trading series

We present an upper bound of cumulative return in financial trading time series to formulate the most possible profit of many trades. The bound can be used to formally analyze the cumulative return varied by the number of trades, the mean return, and transaction cost rate. We also prove and show the validation of the upper bound, and verify the trend of cumulative return is consistent with that of the proposed bound via simulation experiments. Introducing a set of stochastic assessment methodology based on bootstrap into the organization of experimental data, we illustrate the influence on cumulative return from the relationship between the mean of return and transaction cost rate, technical trading rules, and stock indexes. To the best of our knowledge, this is the first to present and prove a bound of cumulative return of a stock trading series in theory. Both theoretical analyses and simulation experiments show the presented bound is a good mathematical tool to evaluate the trading risks and chances using given trading rules in stock trading markets.