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- Accounting for higher moments is an important challenge in portfolio selection. To that aim, two authours proposed to rethink the current paradigm of standard approaches in portfolio optimization where an investor targets a full return distribution based on a reference portfolio instead of a finite number of statistics. In this thesis, we studied the minimum divergence portfolio whose return density minimizes the Kullback-Leibler or Rényi divergences with respect to the target-return density. This approach gives full flexibility in terms of target and is supposed to enhance the higher orders of the portfolio. We observed on an out-of-sample study, that the minimum divergence portfolio generally leads to the same mean-variance trade-off as the reference portfolio but with a significant improvement in higher orders. The minimum divergence portfolio also outperforms portfolio selection techniques that take higher orders into account.