  We developed a strategic of optimal portfolio based on information theory and
Tsallis statistics. The growth rate of a stock market is defined by using
$q$-deformed functions and we find that the wealth after n days with the
optimal portfolio is given by a $q$-exponential function. In this context, the
asymptotic optimality is investigated on causal portfolios, showing advantages
of the optimal portfolio over an arbitrary choice of causal portfolios.
Finally, we apply the formulation in a small number of stocks in brazilian
stock market $[B]^{3}$ and analyzed the results.
