Simulation Methodology for Financial Assets with Imprecise Data

During last decades the stochastic simulation approach, both via Monte Carlo (MC) and Quasi Monte Carlo (QMC) has been vastly applied and subsequently analyzed in almost all branches of science. Very nice applications can be found in areas that rely on modeling via stochastic processes, such as finance. However, since financial quantities, opposed to natural processes, depend on human activity, their modeling is often very challenging. Many scholars therefor suggest to specify some parts of financial models by means of fuzzy set theory. In this contribution the recent knowledge of fuzzy numbers and their approximation is utilized in order to suggest fuzzy-MC simulation to modeling of returns of financial quantities, such as prices of stocks, commodities or exchange rates. Finally, three distinct types of potential fuzzy-stochastic models are suggested, including quantile estimation illustrations.