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In general, traders test their trading strategies by applying them on the historical market data (backtesting), and then apply to the future trades the strategy that achieved the maximum profit on such past data. In this paper, we propose a new trading strategy, called DNN-forwardtesting, that determines the strategy to apply by testing it on the possible future predicted by a deep neural network that has been designed to perform stock price forecasts and trained with the market historical data. In order to generate such an historical dataset, we first perform an exploratory data analysis on a set of ten securities and, in particular, analize their volatility through a novel k-means-based procedure. Then, we restrict the dataset to a small number of assets with the same volatility coefficient and use such data to train a deep feed-forward neural network that forecasts the prices for the next 30 days of open stocks market. Finally, our trading system calculates the most effective technical indicator by applying it to the DNNs predictions and uses such indicator to guide its trades. The results confirm that neural networks outperform classical statistical techniques when performing such forecasts, and their predictions allow to select a trading strategy that, when applied to the real future, increases Expectancy, Sharpe, Sortino, and Calmar ratios with respect to the strategy selected through traditional backtesting.