Profitability in a Multiple Strategy Market

In this paper we extend the definition of martingale to a larger class of processes named m-martingales, motivated by the study of trading-speculation. The link between speculation, profits and strategies is widely studied among financial and economical theorists. The possibility of making profits appears related to the way of making choices on the market (available strategies) more than on the available informations.By outlying different way of making strategies, we point out conditions under which profit may be allowed. Moreover, this class of processes admits medium term arbitrage, which is not allowed by ordinary martingales