Influence of membership function’s shape on portfolio optimization results

Portfolio optimization, one of the most rapidly growing field of modern finance, is selection process, by which investor chooses the proportion of different securities and other assets to held. This paper studies the influence of membership function’s shape on the result of fuzzy portfolio optimization and focused on portfolio selection problem based on credibility measure. Four different shapes of the membership function are examined in the context of the most popular optimization problems: mean-variance, mean-semivariance, entropy minimization, value-at-risk minimization. The analysis takes into account both: the study of necessary and sufficient conditions for the existence of extremes, as well as the statistical inference about the differences based on simulation.