A risk averse robust portfolio optimization under severe uncertainties by using IGDT approach: Iran Stock Exchange

Document Type : Research Paper


1 Department of Industrial Engineering, Faculty of Engineering, Alzahra University, Tehran, Iran

2 Faculty of Industrial Engineering, University of Tehran, Iran


Portfolio optimization in finance and economy is more than a mathematical model for improving performance under uncertainty constraints. Practically all organizations seek to create value by selecting the best portfolios that consume the least resources and obtaining high expected portfolio returns and controlling risk. In the context of the portfolio selection problem, severe uncertainties would significantly affect the technical and financial aspects. This paper presents a bi-level information gap decision theory (IGDT) risk averse decision-making tool for robust portfolio optimization problems to help organizations or investors for managing their portfolios and finding the best transactions with severe uncertainty variables (price and return) to process the forecast data generated by the learning prediction method in order to construct the optimal stock portfolios that a target profit is guaranteed. The heuristic solution approach is constructed and the augmented ε-constraint method is used to solve the proposed bi-level IGDT robust optimization problem. The effectiveness and efficiency of the proposed model are evaluated on the Iranian Stock Market. The results show the efficiency and effectiveness of the proposed model for selecting the best stocks. The Mont Carlo simulation method is applied for the validation of results.


[1] M. Asadujjaman and K. Zaman, Robustness-based portfolio optimization under epistemic uncertainty, J. Ind. Eng. Int. 15 (2019), 207–219.
[2] C. Baudrit, D. Dubois and D. Guyonnet, Joint propagation and exploitation of probabilistic and possibilistic information in risk assessment, IEEE Trans. Fuzzy Syst. 14 (2006), no. 5, 593–608.
[3] A.T. Beck, W.J. Gomes and F.A. Bazgn, On the robustness of structural risk optimization with respect to epistemic uncertainties, Int. J. Uncertain. Quantific.2 (2012), no. 1.
[4] Y. Ben-Haim, Info-gap decision theory: decisions under severe uncertainty, Elsevier, 2006.
[5] D. Berleant, L. Andrieu, J.P. Argaud, F. Barjon, M.P. Cheong, M. Dancre, M., . . . and C.C. Teoh, Portfolio management under epistemic uncertainty using stochastic dominance and information-gap theory, Int. J. Approx. Reason. 49 (2008), no. 1, 101–116.
[6] V. Boasson, E. Boasson and Z. Zhou, Portfolio optimization in a mean-semivariance framework, Invest. Manag. Financ. Innov. 8 (2011), no. 3, 58–68.
[7] G. Bormetti, M.E. De Giuli, D. Delpini and C. Tarantola, Bayesian value-at-risk with product partition models, Quant. Finance 12 (2012), no. 5, 769–780.
[8] G.W. Brown and M.T. Cliff, Investor sentiment and the near-term stock market, J. Empir. Finance 11 (2004), no. 1, 1–27.
[9] L.A.S. Camargo, L.D. Leonel, D.S. Ramos and A.G.D. Stucchi, A risk averse stochastic optimization model for wind power plants portfolio selection, Int. Conf. Smart Energy Syst. Technol., IEEE, 2020), pp. 1–6.
[10] Z. Chen and P.J. Knez, Portfolio performance measurement: Theory and applications, Rev. Financ. Stud. 9 (1996), no. 2, 511–555.
[11] M.P. Cheong, G.B. Sheble, D. Berleant, C.C. Teoh, J.P. Argaud, M. Dancre, L. Andrieu and F. Barjon, Second order stochastic dominance portfolio optimization for an electric energy company, IEEE Lausanne Power Tech. 2007 (2007), 819–824.
[12] L.B. Chincarini, Quantitative equity portfolio management: An active approach to portfolio construction and management, McGraw-Hill, 2006.
[13] Z. Dai, D. Li and F. Wen, Worse-Case Conditional Value-at-Risk for Asymmetrically Distributed Asset Scenarios Returns, J. Comput. Anal. Appl. 20 (2016), no. 1.
[14] E. Delage and Y. Ye, Distributionally robust optimization under moment uncertainty with application to datadriven problems, Oper. Res.58 (2010), no. 3, 595–612.
[15] D. Desai, G. Wu and M.H. Zaman, Tackling HIV through robust diagnostics in the developing world: current status and future opportunities, Lab Chip 11 (2011), no. 2, 194–211.
[16] M. Esmaili, N. Amjady and H.A. Shayanfar, Multi-objective congestion management by modified augmented εconstraint method, Appl. Energy 88 (2011), no. 3, 755–766.
[17] M. Fereiduni and K. Shahanaghi, A robust optimization model for distribution and evacuation in the disaster response phase, J. Ind. Engin. Int. 13 (2017), no. 1, 117–141.
[18] A. Fertis, M. Baes and H.J. L¨uthi, Robust risk management, Eur. J. Oper. Res. 222 (2012), no. 3, 663–672.
[19] A. Ghadimi Hamzehkolaei, G. Ghodrati Amiri, A. Gharagozlu, A. Vafaeinezhad and A. Zare Hosseinzadeh, Seismic zoning of urban areas considering the effect of physical conditions using Fuzzy logic theory: case study of Tehran’s 7th region, J. Struct. Construct. Engin. 5 (2018), no. 3, 5–15.
[20] J.W. Goh, K.G. Lim, M. Sim and W. Zhang, Portfolio value-at-risk optimization for asymmetrically distributed asset returns, Eur. J. Oper. Res. 221 (2012), no. 2, 397–406.
[21] A. Hafezalkotob, A. Hami-Dindar, N. Rabie and A. Hafezalkotob, A decision support system for agricultural machines and equipment selection: A case study on olive harvester machines, Comput. Electron. Agricul. 148 (2018), 207–216.
[22] J.C. Helton, Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal, Reliab. Engin. Syst. Safety 42 (1993), no. 2-3, 327–367.
[23] B.L. Hu and E. Verdaguer, Stochastic gravity: Theory and applications, Liv. Rev. Relat. 11 (2008), no. 1, 1–112.
[24] G.B. Huang, Q.Y. Zhu and C.K. Siew, Extreme learning machine: theory and applications, Neurocomput. 70 (2006), no. 1-3, 489–501.
[25] H. Jin, Z. Quan Xu and X. Yu Zhou, A convex stochastic optimization problem arising from portfolio selection, Math. Finance: Int. J. Math. Statist. Financ. Econ. 18 (2008), no. 1, 171-183.
[26] A.R. Jordehi, M.S. Javadi, M. Shafie-khah and J.P. Catallo, Information gap decision theory (IGDT)-based robust scheduling of combined cooling, heat and power energy hubs, Energy 231 (2021), 120918.
[27] N. Khalaj, N.A. Abu Osman, A.H. Mokhtar, M. Mehdikhani and W.A.B. Wan Abas, Balance and risk of fall in individuals with bilateral mild and moderate knee osteoarthritis, PloS one 9 (2014), no. 3, 92270.
[28] H. Konno and T. Koshizuka, Mean-absolute deviation model, Iie Trans. 37 (2005), no. 10, 893–900.
[29] M. Labb´e, P. Marcotte and G. Savard, A bilevel model of taxation and its application to optimal highway pricing, Manag. Sci. 44 (1998), no. 12-part-1, 1608–1622.
[30] G. F. Loewenstein, E. U. Weber, Ch. K. Hsee and N. Welch, Risk as feelings, Psych. Bull. 127 (2001), no. 2, 267.
[31] V.W. Lui, M.L. Hedberg, H. Li, B.S. Vangara, K. Pendleton, Y. Zeng, . . . and J.R. Grandis, Frequent Mutation of the PI3K Pathway in Head and Neck Cancer Defines Predictive BiomarkersMutation of PI3K Pathway in Head and Neck Cancer, Cancer Discov. 3 (2013), no. 7, 761–769.
[32] M. Majidi, B. Mohammadi-Ivatloo and A. Soroudi, Application of information gap decision theory in practical energy problems: A comprehensive review, Appl. Energy 249 (2019), 157–165.
[33] H. Markowitz, The utility of wealth, J. Ppolitic. Econ. 60 (1952), no. 2, 151–158.
[34] W. Markowitz, Variations in rotation of the earth, results obtained with the dual-rate moon camera and photographic zenith tubes, Symp. Int. Astronom. Union, Cambridge University Press, 11 (1959), 26–33.
[35] M. Mehrbod, N. Tu and L. Miao, A hybrid solution approach for a multi-objective closed-loop logistics network under uncertainty, J. Ind. Engin. Int. 11 (2015), no. 2, 237–252.
[36] Y. Merzifonluoglu, Risk averse supply portfolio selection with supply, demand and spot market volatility, Omega 57 (2015), 40–53.
[37] A. Meucci, Risk and asset allocation, Springer, New York, 2005.
[38] W.L. Oberkampf, S.M. DeLand, B.M. Rutherford, K.V. Diegert and K.F. Alvin, Error and uncertainty in modeling and simulation, Reliab. Engin. Syst. Safety 75 (2002), no. 3, 333–357.
[39] N.P. O’Dowd, Y. Lei and E. P. Busso, Prediction of cleavage failure probabilities using the Weibull stress, Engin.Fracture Mech. 67 (2000), no. 2, 87–100.
[40] Z. Qin, S. Kar and H. Zheng, Uncertain portfolio adjusting model using semiabsolute deviation, Soft Comput. 20 (2016), no. 2, 717–725.
[41] R.T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, J. Risk 2 (2000), 21–42.
[42] S.A. Ross, The determination of financial structure: the incentive-signalling approach, Bell J. Econ. 8 (1977), no. 1, 23–40.
[43] P.A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Stochastic Optimization Models in Finance (1975), 517–524.
[44] S. Sarykalin, G. Serraino and S. Uryasev, Value-at-risk vs. conditional value-at-risk in risk management and optimization, State-of-the-art decision-making tools in the information-intensive age, Informs (2008), 270–294.
[45] C. Skiadas, Dynamic portfolio choice and risk aversion, Oper. Res- Manag. Sci. 15 (2007), 789–843.
[46] W. F. Sharpe, Mean-absolute-deviation characteristic lines for securities and portfolios, Manag. Sci. 18 (1971), no. 2, B-1.
[47] T. Sriyakul and K. Jermsittiparsert, Risk-constrained design of autonomous hybrid refueling station for hydrogen and electric vehicles using information gap decision theory, Int. J. Hydrogen Energy 46 (2021), no. 2, 1682-1693.
[48] R. S. Tsay, Analysis of financial time series, John wiley & sons, 2005.
[49] S. Uryasev and P. M. Pardalos, Stochastic optimization: algorithms and applications, Springer Sci. Bus. Media 54 (2013).
[50] Z. Vafaeinezhad, Z. Kazemi, M. Mirmoeini, H. Piroti, E. Sadeghian, M. Mohammad Ali-Vajari, . . . and M. Jafari, Trends in cervical cancer incidence in Iran according to national cancer registry, J. Mazandaran Univer. Med. Sci.28 (2018), no. 161, 108–114.
[51] S. Yoo, S. Jeon, S. Jeong, H. Lee, H. Ryou, T. Park, . . . and K. Oh, Prediction of the change points in stock markets using DAE-LSTM, Sustainability 13 (2021), no. 21, 11822.
[52] S. Zaman and D. Grosu, Combinatorial auction-based allocation of virtual machine instances in clouds, J. Paral. Distrib. Comput. 73 (2013), no. 4, 495–508.
[53] S. Zymler, D. Kuhn and B. Rustem, Worst-case value at risk of nonlinear portfolios, Manag. Sci. 59 (2013), no. 1, 172- 188.
Volume 14, Issue 4
April 2023
Pages 359-385
  • Receive Date: 01 December 2021
  • Revise Date: 03 January 2022
  • Accept Date: 11 February 2022
  • First Publish Date: 20 September 2022