Portfolio Theory, Information Theory and Tsallis Statistics

Abstract

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.