Value at risk methodology under soft conditions approach (fuzzy-stochastic approach)

The paper describes methodology of dealing with financial modelling under uncertainty with risk and vagueness aspects. An approach to modelling risks by the Value at Risk methodology under imprecise and soft conditions is solved. It is supposed that the input data and problem conditions are difficult to determine as real numbers or as some precise distribution function. Thus, vagueness is modelled through the fuzzy numbers of the linear T-number type. The combination of risk and vagueness is solved by fuzzy-stochastic methodology. Illustrative example is introduced.