Fuzzy Expected Value-Deviation Portfolio Selection with Riskless Asset Based on Credibility Measures

This paper explores a problem whether a portfolio should contain a riskless asset in fuzzy environment based on credibility theory. From a novel perspective, we use the fuzzy deviation together with value function (value-deviation) as a novel portfolio risk measurement. In the light of credibility theory in this paper, three credibilistic expected value-deviation models with fuzzy returns are proposed for the first time. In addition, genetic algorithm is adopted to solve our presented fuzzy nonlinear portfolio models. Furthermore, a comparative numerical example with or without a riskless asset is given to verify the validity of our presented portfolio models. The final results present that no matter how much return investors want to realize, the maximum value deviation of portfolio with a riskless asset is more than the maximum value deviation of portfolio without a riskless asset forever. That enriches portfolio contents in theory and provides investors with more choices in practice.