fuzzy random variable; fuzzy quantile; fuzzy stochastic process; Value at Risk estimation; backtesting;

Since financial quantities - opposed to natural processes - depend on human activity, their modeling is often very challenging. Many scholars therefore suggest for some cases, such as illiquid positions, newly introduced securities or instable market condition, to specify some parts of financial models by means of fuzzy set theory. In this paper we formulate a fuzzy-stochastic model of risk estimation to be solved by simulation approach. The application possibility is shown for the case of market (FX rate) risk and its subsequent backtesting. Although a single position is considered, it can be easily generalized to deal with more complex problem.