In this paper we propose a financial trading system whose strategy is developed by means of an artificial neural network approach based on a recurrent reinforcement learning algorithm. In general terms, this kind of approach consists in specifying a trading policy based on some predetermined investor’s measure of profitability, and in setting the financial trading system while using it. In particular, with respect to the prominent literature, in this contribution: first, we take into account as measure of profitability the reciprocal of the returns weighted direction symmetry index instead of the wide-spread Sharpe ratio; second, we obtain the differential version of this measure of profitability and obtain all the related learning relationships; third, we propose a procedure for the management of drawdown-like phenomena; finally, we apply our financial trading approach to some of the major world financial market indices.