Document Type : Original Article
Authors
1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Guilan, Iran.
2 Department of Statistics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
3 Department of Statistics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran.
Abstract
Value at Risk (VaR) is a key measure in financial risk management. However, traditional VaR models are often challenged by the inherent uncertainty and ambiguity in market data. This paper introduces a novel method for estimating VaR under fuzzy conditions to address this limitation. In this study, we consider a linear portfolio consisting of ten stocks whose returns are imprecise and vague. To handle this vagueness, we assume that the portfolio returns follow a normal distribution and are represented as triangular fuzzy numbers. The proposed method employs α-cut sets to compute the fuzzy VaR for the portfolio. Additionally, we use daily log returns to estimate the returns for each stock over the specified period. By applying this method, we can calculate the lower and upper bounds, as well as the core values of the α-cuts, for the fuzzy VaR metric of the portfolio. The numerical results demonstrate that fuzzy VaR yields more accurate estimates compared to traditional VaR. This study illustrates how fuzzy VaR techniques improve decision making under ambiguity by providing a more realistic representation of financial uncertainty.
Keywords
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