Estimating Portfolio Value-at-Risk and Expected Shortfall by Possibility and Necessity Theory

One of the main concerns of investors and financial managers is the way of dealing with investment risk; thus identification, calculation and management of risk are important issues in financial fields. So, in this study, the portfolio value-at-risk and expected shortfall are estimated by considering uncertainty in risk factors. The concept of fuzzy random variable, specifically possibility and necessity theory, is used to face uncertainty in financial data. In the following, the terms of fuzzy value-at-risk and expected shortfall introduced with assuming normal and t-student distribution and considering both state of fixed and stochastic for uncertainty factor. The results indicate that assumptions of t-student distribution and stochastic uncertainty factor make the estimation of both risk measures to be more conservative.