Providing an Optimal Robust Portfolio Model with Mean- CVaR Approach

محورهای موضوعی : Financial Mathematics

Fatemeh Pouraskari Jourshari ¹ (Department of Financial Engineering, Rasht Branch, Islamic Azad University, Rasht, Iran)
Mohsen Khodadadi ² (Department Of Accounting, Roudsar and Amlash Branch, Islamic Azad University, Roudsar, Iran)
Seyed Reza Seyed Nejad Fahim ³ (Department of Accounting, Lahijan Branch, Islamic Azad University,Lahijan, Iran)

تاریخ دریافت : 1400/04/12 تاریخ پذیرش : 1400/06/13 تاریخ انتشار : 1401/10/11

کلید واژه: Uncertain, Mean- CVaR, Linear model, Robust Optimization,

چکیده مقاله :

The portfolio selection problem is one of the main investment management prob-lems. In the portfolio selection problem, robustness is sought against uncertainty or variability in the value of the parameters of the problem. This paper has been conducted for Robust portfolio optimization based on the mean-cvar approach. And introduces the linear mean-cvar model as a criterion for calculating risk and provides an optimal Robust mean-cvar model. Robust approach used in this research is the Bertsimas and Sim. In this approach, Robust counterpart presented for a linear programming model remains linear, maintaining the advantages of the linear programming model in the optimal model. The model developed in this research is randomly selected by real data of 20 stocks of the S&P 500 index for three years, this development help portfolio selection problem to consider uncertainty. Interval optimization is modeling approach to consider parameters uncertainty in this paper. Considering uncertainty make model more realistic. The results of model show that this approach has computational efficiency and on the other hand proposed model produce better solution in risk and portfolio rate of return point of view

منابع و مأخذ:

 [1] Ben-Tal, A., Nemirovski, A., Robust Solutions of Linear Programming Problems Contaminated with Uncertain Data, Mathematical Programming, 2000, 88, P.411–24. Doi:10.1007/PL00011380

[2] BenTal, A., Nemirovski, A., Robust optimization – methodology and applications, Math. Program, Ser. 2002 92, P453–480 Doi:10.1007/s101070100286

[3] Bertsimas, D., Sim, M., The price of Robustness; Operations Research, 2004, 52, P.35–53, Doi:10.1287 / opre. 1030.0065

[4] Chen, W., Tan, S., Robust Portfolio Selection Based on Asymmetric Measures of Variability of Stock Returns, Journal of Computational and Applied Mathematics, 2009, 232, P.295-304. Dio: 10.4028/ www. scientific.net. 543-547.1811

[5] El Ghaoui, L., Oks, M., Oustry, F., Worst-case Value-at-risk and Robust Portfolio Optimization; A Conic Programming Approach, Operations Research, 2003, 51, P.543–56. Doi=10.1.1.154.9174&rep.

[6] Ezaei, N., Elmi, Z., Behavioral Finance Models and Behavioral Biases in Stock Price Forecasting, Advances in Mathematical Finance and Applications, 2018, 3(4), P.67-82. Doi: 10.22034/amfa.2019.576127.1118

[7] Gaivoronski, A.A., Pflug, G.,Value at risk in portfolio optimization: properties and computational aproach, 2005, 7, P. P1-31. Doi:10.21314/JOR.2005.106.

[8] Goldfarb, D., Iyengar, G., Robust portfolio selection problems, Math. Oper. Res, 2001, 28, Doi: 10.1287/ moor.28.1.1.14260

[9] Kawas, B., Thiele, A., A Log-robust Optimization Approach to Portfolio Management, Working Paper, 2008, 33, P. 207-233. Doi:10.1007/s00291-008-0162-3

[10] Liwei, Ju, Qin,liang,Tan.Yan, Lu.Zhongfu,Tan.Yuxie,Zhang.Qing,kunTan., A CVaR-robust-based multi-objective optimization model and three-stage solution algorithm for a virtual power plant considering uncertainties and carbon emission allowances, International Journal of Electrical Power & Energy Systems, 2019, 107, P.628-643. Doi:10.1016/j.ijepes.2018.12.012

[11] Miryekemami, S., Sadeh, E., Sabegh, Z.,  Using Genetic Algorithm in Solving Stochastic Programming for Multi-Objective Portfolio Selection in Tehran StockExchange, Advances in Mathematical Finance and Applications, 2017, 2(4), P.107-120. Doi: 10.22034/AMFA.2017.536271.

[12] Moon, Y., Yao, T. A., Robust Mean Absolute Deviation Model for Portfolio Optimization; Computers and Operations Research, 2011, 38, P.272-281. Dio:1251–1258. 10.1016/j.cor.2010.10.020

[13] Navidi, s., Rostamy-Malkhalifeh, M., Banilashemi, SH., Using MODEA and MODM with Different Risk Measures for  Portfolio Optimization, Advances in Mathematical Finance, 2020, 5(1), P.29-51.

 Doi: 10.22034/amfa.2019.1864620.1200

[14] Pflug, G.Ch., Some remarks on the value at risk and the conditional value at risk. In: Uryasev, S. (Ed.), Probabilistic Constrained Optimization: Methodology and Applications. Kluwer Academic Publishers2000, 49, P,272-281. Doi:10.1007/978-1-4757-3150-7_15

[15] Rockafellar, R.T., Uryasev, S.,Conditional value at risk for general loss distributions. J. Bank. Financ.2002 26, P.1443–1471. Doi:10.1016/S0378-4266(02)00271-6

[16] Rockafellar, R.T., Uryasev, S., Optimization of conditional value at risk. Mahdi.Maybee, Bryan. Whale,Jonathan. McHugh,Adam. Climate Policy Uncertainty and  ShahNazari 2000, 21–4.

[17] Power Generation Investments: A Real Options-CVaR Portfolio Optimization Approach, 2015, 75, P.2649-2657. Doi: 10.1155/2021/8863597.

[18] Soyster, A.L., Convex Programming with Set-inclusive Constraints and Applications to Inexact Linear Programming, Operations Research,1973, 21, P.54–7. Doi: 10.1287/opre.21.5.1154

[19] Tao, Liangyan, Liu, Sifeng, Xie, Naiming. Ahmedjavad,saad., Optimal position of supply chain delivery window with risk-averse suppliers: A CVaR optimization approach, International Journal of Production Economics 2021, 232, Doi: 10.1016/j.ijpe.2020.107989

[20] Tutuncu, R., Koenig, M., Robust Asset Allocation; Annals of Operations Research, 2004, 132, P.157–87. Doi:10.1023/B:ANOR.0000045281.41041.

[21] Vladimirou, H., Brief introduction to stochastic programming (and financial modeling applications), HERMES, CCFE, School of Economics and Management, University of Ciprus, 2003. 17. Doi: 10.1007/978-1-4614-0237-