Abstract: 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 is 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.

Abstract: Abstract The valuing of a firm equity as a call option is a crucial problem in financial decision-making. There are two basic aspects that are studied; contingent claim features (payoff functions) and risk (stochastic process of underlying assets). However, non-preciseness (vagueness, uncertainty) of input data is often neglected. Thus, a combination of risk (stochastic) and uncertainty (fuzzy instruments) could be a useful approach in calculating a firm value as a call option. The Black–Scholes methodology of appraising equity as a European call option is applied. Fuzzy–stochastic methodology under fuzzy numbers (T-numbers) is proposed and described. Fuzzy–stochastic model of appraising a firm equity is proposed. Input data are in a form of fuzzy numbers and result, firm possibility-expected equity value is also determined vaguely as a fuzzy set. Illustrative example is introduced.