A random-fuzzy portfolio selection DEA model using value-at-risk and conditional value-at-risk

The complexity involved in portfolio selection has resulted in the development of a large number of methods to support ambiguous financial decision making. We consider portfolio selection problems where returns from investment securities are random variables with fuzzy information and propose a data envelopment analysis model for portfolio selection with downside risk criteria associated with value-at-risk (V@R) and conditional value-at-risk (CV@R). Both V@R and CV@R criteria are used to define possibility, necessity, and credibility measures, which are formulated as stochastic nonlinear programming programs with random-fuzzy variables. Our constructed stochastic nonlinear programs for analyzing portfolio selection are transformed into deterministic nonlinear programs. Moreover, we show an enumeration algorithm can solve the model without any mathematical programs. Finally, we demonstrate the applicability of the proposed framework and the efficacy of the procedures with a numerical example.