Before revision: Tsallis relative entropy , which is the generalization of Kullback-Leibler relative entropy  to non-extensive systems, is investigated as a possible risk measure in constructing risk optimal portfolios whose returns beat market returns.
After revision: Tsallis relative entropy , which is the generalization of Kullback-Leibler relative entropy (KLRE) to non-extensive systems, is investigated as a possible risk measure in constructing risk optimal portfolios whose returns beat market returns.