Investment portfolio optimization using value at risk under credibility theory with Z-numbers approach

Z-numbers theory was proposed in 2011 by Lotfy Zadeh. This theory describe the uncertainty of information where any z-number is displayed by a pair of fuzzy number. Because of the uncertainty in the financial markets, this theory can be used in the investment portfolio selection. As the first component of z-number is the fuzzy asset return and the second component is reliability of prediction of first component. We can use value at risk criterion for increasing efficiency of investment portfolio selection model. Due to consideration the uncertainty in asset returns and using value at risk, this model is an appropriate model for investment portfolio selection. The advantage of this method compared to the conventional fuzzy method is consideration uncertainty of expert knowledge and allocation reliability to their prediction of fuzzy parameter. Finally, we provide a numerical example from Tehran stock market.