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Fuzzy Estimation of Value at Risk for a Portfolio with Triangular Fuzzy Returns | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 6، شماره 2، مهر 2026، صفحه 97-123 اصل مقاله (935.6 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2026.89886.1242 | ||
| نویسندگان | ||
| Batoul Salamah1؛ Reza Zarei* 2؛ Farshid Mehrdoust1؛ Mohammad Ghasem Akbari3 | ||
| 1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Guilan, Iran. | ||
| 2Department of Statistics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. | ||
| 3Department of Statistics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Fuzzy value at risk؛ α-cuts sets؛ Variance-covariance method؛ Portfolio model؛ Triangular fuzzy return | ||
| مراجع | ||
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[1] P. Abad, S. Benito, and C. L´opez, A comprehensive review of Value at Risk methodologies, The Spanish Review of Financial Economics, 12(1) (2014), 15-32. [2] E. Abasi, B. Teimurpur, and M. Barjesteh Maleki, Optimum portfolio selection using value at risk in Tehran Stock Exchange, Journal of Economic Research (Tahghighat-EEghtesadi), 44(2), (2010). [3] Basle Committee on Banking Supervision (Basle Committee), Amendment to the Capital Accord to Incorporate Market Risks, Base: Basle Committee on Banking Supervision (January), (1996). [4] P. Best, Implementing value at risk, John Wiley and Sons, (1998). [5] U. Cherubini, and G. Della Lunga, Fuzzy value-at-risk: accounting for market liquidity, Economic Notes, 30(2), (2001), 293-312. [6] R. Campbell, R. Huisman, and K. Koedijk, Optimal portfolio selection in a Value-at-Risk framework, Journal of Banking and Finance, 25(9), (2001), 1789-1804. [7] T. Coleman, A practical guide to risk management, CFA Institute Research Foundation,(2011), M2011-2. [8] G. Dionne, Risk management: History, definition, and critique, Risk management and insurance review, 16(2), (2013), 147-166. [9] X. Deng, and W. Li, A novel probabilistic hesitant fuzzy portfolio selection model with value-at-risk and safety level of score, Engineering Computations, 38 (5), (2021) 2137-2162. [10] D. Dubois, and H. Prade, Operations on fuzzy numbers, International Journal of systems science, 9(6), (1978), 613-626. [11] S. Emmer, M. Kratz, and D. Tasche, What is the best risk measure in practice? A comparison of standard measures, SSRN Electronic Journal, Jan, (2013), 1312.1645. [12] M. L. Guerra, and L. Sorini, Value at risk based on fuzzy numbers, Axioms, 9(3), (2020), 98. [13] O. L. Gebizlioglu, B. ¸Seno˘glu, and Y. M. Kantar, Comparison of certain value-at-risk estimation methods for the two-parameter Weibull loss distribution, Journal of Computational and Applied Mathematics, 235(11), (2011), 3304-3314. [14] J. Gayt´an Cort´es, Value at Risk (VaR), Mercados Y Negocios, (2022), 95-106. [15] J. C. Hull, “Options, futures, and other derivatives”, AMBER – ABBS Management Business and Entrepreneurship Review, 7(1), (2016), 70. [16] F. Hooshmand, Z. Anoushirvani, and S. A. MirHassani, Model and efficient algorithm for the portfolio selection problem with real-world constraints under value-at-risk measure, International Transactions in Operational Research, 30(5), (2023), 2665-2690. [17] P. Jorion, Value at risk: the new benchmark for managing financial risk, New York: McGraw-Hill, (2000). [18] F. H. Knight, Risk, uncertainty and profit, Houghton Mifflin, (1921). [19] M. B. Kar, S. Kar, S. Guo, X. Li, and S. Majumder, A new bi-objective fuzzy portfolio selection model and its solution through evolutionary algorithms, Soft Computing, 23(12), (2018), 4367–4381. [20] J. Longerstaey, and M. Spencer, RiskMetrics—Technical document, New York: Risk-Metrics Group, J.P. Morgan, 1996. [21] W. Liu, A. Semeyutin, C. K. M. Lau, and G. Gozgor, Forecasting value-at-risk of cryptocurrencies with riskmetrics type models, Research in International Business and Finance, 54, (2020), 101259. [22] J. Luki´c, M. Misita, D.D. Milanovi´c, A. Borota-Tiˇsma, and A. Jankovi´c, Determining the risk level in client analysis by applying fuzzy logic in insurance sector, Mathematics, 10(18), (2022), 3268. [23] Y. Liu, H. Ahmadzade, and M. Farahikia, Portfolio selection of uncertain random returns based on value at risk, Soft Computing-A Fusion of Foundations, Methodologies and Applications, 25(8), (2021). [24] H. Markowitz, Portfolio Selection, The Journal of Finance, 7(1), (1952), 77–91. [25] J. P. Morgan, RiskMetrics Technical Document, New York: Morgan Guaranty Trust Company, (October), (1994). [26] A. M. Moussa, J. S. Kamdem, and M. Terraza, Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns, Economic Modelling, 39, (2014), 247-256. [27] L. Maciel, R. Ballini, and F. Gomide, An evolving possibilistic fuzzy modeling approach for value-at-risk estimation, Applied Soft Computing, 60, (2017), 820-830. [28] N. Pearson, Risk Budgeting: Portfolio Problem Solving with Value-at-Risk, John Wiley and Sons, Hoboken, 2002. [29] M. Pourrafiee, A. Nafei, S. Banihashemi, and S. P. Azizi, Comparing entropies in portfolio diversification with fuzzy value at risk and higher-order momen, Fuzzy information and engineering, 12(1), (2020), 123-138. [30] A. Pe˜na, I. Bonet, C. Lochmuller, H. A. Pati˜no, F. Chiclana, and M. G´ongora, A fuzzy credibility model to estimate the Operational Value at Risk using internal and external data of risk events, Knowledge-Based Systems, 159, (2018), 98-109. [31] J. E. M. Reyes, J. J. C. P´erez, and S. C. Ak´e, Credit risk management analysis: An application of fuzzy theory to forecast the probability of default in a financial institution, Contadur´ıa Y Administraci´on, 69(1), (2023), 430. [32] R. Shayya, M. T. Sorrosal-Forradellas, and A. Terce˜ A±o, Value-at-risk models: a systematic review of the literature, Journal of Risk, (2023). [33] K. Shang, and Z. Hossen, Applying fuzzy logic to risk assessment and decision-making, Casualty Actuarial Society, Canadian Institute of Actuaries, Society of Actuaries, (2013), 1-59. [34] R. K. Shiraz, M. Tavana, and H. Fukuyama, A random-fuzzy portfolio selection DEA model using value-at-risk and conditional value-at-risk, Soft Computing, 24(22), (2020), 17167-17186. [35] G. Sathvika, N. Suresh, and D. Thavva, A Study On Value At Risk (VAR) Models In Measuring Market Risk, International Journal of Research Publication and Reviews, 6, (2025), 5976-5980. [36] S. Taghikhani, F. Baroughi, and B. Alizadeh, Mean–variance value at risk criterion for solving a p-median location problem on networks with type-2 intuitionistic fuzzy weights, Journal of Computational and Applied Mathematics, 437, (2024), 115481. [37] B. Wang, S. Wang, and J. Watada, Fuzzy portfolio selection based on value-at-risk, In 2009 IEEE International Conference on Systems, Man and Cybernetics, IEEE, (2009, October), (pp. 1840-1845). [38] H. C. Wu, The fuzzy estimators of fuzzy parameters based on fuzzy random variables, European Journal of Operational Research, 146(1), (2003), 101-114. [39] B. Wang, Y. Li, S. Wang, and J. Watada, A multi-objective portfolio selection model with fuzzy value-at-risk ratio, IEEE Transactions on Fuzzy Systems, 26(6), (2018), 3673-3687. [40] D. Wang, Y. Chen, H. Wang, and M. Huang, Formulation of the non-parametric value at risk portfolio selection problem considering symmetry, Symmetry, 12(10), (2020), 1639. [41] Y. Wang, X. Qi, S. Qin, Calculation of VaR — Based on the Account Manager’s Perspective, Modern Economics and Management Forum, 5, (2024), 442. [42] Y. Yoshida, An estimation model of value-at-risk portfolio under uncertainty, Fuzzy Sets and Systems, 160(22), (2009), 3250-3262. [43] L. A. Zadeh, Fuzzy sets, Information and control, 8(3), (1965),338-353. [44] Z. Zmeˇskal, Value at risk methodology of international index portfolio under soft conditions (fuzzy-stochastic approach), International Review of Financial Analysis, 14(2),(2005), 263-275. [45] H. Zhang, J. Watada, and B. Wang, Sensitivity-based fuzzy multi-objective portfolio model with Value-at-Risk, IEEJ Transactions on Electrical and Electronic Engineering, 14(11), (2019), 1639-1651. [46] Y. Zhang, W. Liu, and X. Yang, An automatic trading system for fuzzy portfolio optimization problem with sell orders, Expert Systems with Applications, 187, (2022), 115822. [47] P. Zhao, and Q. Xiao, Portfolio selection problem with Value-at-Risk constraints under non-extensive statistical mechanics. Journal of computational and applied mathematics, 298, (2016), 64-71. | ||
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