Value at Risk in Fuzzy Environment and its Applications

The classical Value at Risk models are considered one of the most widely used metrics for quantifying potential losses in markets under normal market conditions. However, due to the inherent uncertainty and vagueness in financial data, it is often impossible to accurately measure the extent of losses. In this paper, we introduce a novel method to estimate the Value at Risk criterion for a portfolio model under fuzzy conditions. For this purpose, we employ a-cut sets for computing fuzzy Value at Risk. Furthermore, we consider that the portfolio's returns are triangular fuzzy numbers and identically distributed with a normal distribution. In this method, we determine the lower and upper bounds, as well as the central value, for the portfolio's fuzzy value at risk. The numerical results indicate that the fuzzy Value at Risk provides more accurate estimates than the crisp Value at Risk. This study demonstrates how a fuzzy Value at Risk enhances risk assessment, raising the possibility of using it for portfolio optimization and uncertain financial decision-making.

کلیدواژه ها:

Fuzzy Value at Risk ، a-cut sets ، Fuzzy returns ، Variance- covariance method ، Triangular fuzzy number