Multi-objective possibility model for selecting the optimal stock portfolio

Subject Areas : Financial Engineering

Abdolmajid Abdolbaghi Ataabadi ¹ , Alireza Nazemi ² , Masoumeh Saki ³

1 - management, Faculty of Industrial Engineering and Management , shahrood university of technology
2 - Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
3 - Department of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran

Received: 2022-02-19 Accepted : 2022-07-25 Published : 2023-05-01

Keywords: Mean-variance model, Objective functions, Possibility space, Optimal portfolio,

Abstract :

In this paper, we use fuzzy numbers and possibility theory to model possibility. The purpose of this work is to determine the optimal investment model based on the neural network method for fuzzy LR, trapezoidal and triangular numbers in an optimal portfolio. It is listed on the Tehran Stock Exchange to maximize "returns" and reduce "risk" to find the optimal portfolio. Therefore, to achieve this goal, the problem of multi-objective nonlinear programming is addressed. Also, by substituting the mean-variance model and the standard mean deviation instead of the Markowitz mean-variance model, the selection of the optimal portfolio in the possible space is examined. Finally, after calculating the model of the possibility of fuzzy numbers, we reach the optimal stock portfolio, which can be used to set the stock portfolio that has the highest returns and the lowest risk.

References:

[1] Cesarone, F., Scozzari, A., Tardella, F., Efficient algorithms for mean-variance portfolio optimization with hard real-world constraints, Giornale Dell'Istituto Italiano Degli Attuari,  2009, 72, P. 37-56.

 

[2] Balderas, F., Fernandez, E., Gomez, C., Rangel, N., Cruz-Reyes, L., An interval-based approach for evolutionary multi-objective optimization of project portfolios, Int. J. Inf. Technol. Decis. Mak, 2019, 18, P.1317–1358. Doi: 10.1142/S021962201950024X

 

[3] Mercangoz, B. A., Portfolio optimization, International Series in Operations Research and Management Science, 2021, 306, P.15–27.

 

[4] D. Dubois, H., Prade, Posibility Theory, Planum Perss, New York, 1998.

Doi:10.1007/978-1-4614-1800-9_139.

 

[5] Fng, S. C., Rajasekera, J. R., Tsao, H. S. J., Entropy optimization and mathematical programming, Kluwer Academic Publisheres, 1997.

 

[6] Gu., Qiupeng, Xuan., Zuxing, a new approach for ranking fuzzy numbers based on possibility theory, Journal of Computational and Applied Mathematics, 2017, 309, P.674-682. Doi:10, 1016/j.cam.2016,05,017.

 

[7] Hanss, M., Applied fuzzy arithmetic, An introduction with engineering applications, Berlin Heidelberg: Springer, 2005. Doi:10.1007/b138914.

 

[8] Konno, H., Yamazaki,  H., Mean absolute deviation portfolio optimization model and its application to Tokyo stock exchange, Management Science 1997, 37 , P.519-531. Doi: 10.1287/mnsc.37.5.519.

 

[9] Hui-Shan Lee, Fan-Fah Cheng , Shyue-Chuan Chong, Markowitz Portfolio Theory and Capital Asset Pricing Model for Kuala Lumpur Stock Exchange: A Case Revisited, International Journal of Economics and Financial Issues, 2016, 6(S3), P.59-65.

 

[10] Inuiguchi, M., Tanino, T., Portfolio selection under independent possibilistic information, Fuzzy Sets Systems, 2000, 115(1), P.83–92. Doi: 10.1016/S0165-0114(99)00026-3.

 

[11] Izadikhah, M., Group decision making process for supplier selection with TOPSIS method under interval-valued intuitionistic fuzzy numbers. Adv. Fuzzy Sys. 2012, 2, Doi: 10.1155/2012/407942

 

[12] Kapur, J. N., Maximum entropy models in science and engineering, New Delhi: Wiley Eastern Limited, 1990.

 

[13] Klir, G. J., Yuan, B., Fuzzy sets and fuzzy logic, Upper Saddle Rives, NJ: Prentice-Hall, 1995.

 

[14] Lai, K. K., Wang, S. Y., Xu, J. P., Zhu, S. S., Fang, Y., A class of linear interval programming problems and its application to portfolio selection, IEEE Transactions on Fuzzy Systems, 2002, 10(6), P.698-704. Doi:10.1109/TFUZZ.2002.805902.

 

[15] Liu, Y. J., Zhang, W. G., Fuzzy portfolio optimization model under real constraints, Insurance: Mathematics and Economics, 2013, 53(3), P.704-711. Doi: 10.1016/j.insmatheco.2013.09.005.

 

[16] Leo´n. T., Liem. V., Vercher. E., Viability of infeasible portfolio selection problems: A fuzzy approach, European Journal of Operational Research, 2002, 139(1), P.178–189. Doi: 10.1016/S0377-2217(01)00175-8.

 

[17] Lobo, M. S., Fazel, M., Boyd, S., Portfolio optimization with linear and fixed transaction costs, Annals of Operations Research, 2007, 152(1), P.341-365. Doi:10.1007/s10479-006-0145-1.

 

[18] Pedersen, L. H., Babu, A., Levine, A., Enhanced portfolio optimization, Financial Analysts Journal, 2021, 77(2), P.124–151.  Doi: 10.1080/0015198X.2020.1854543.

[18] Mart´ınez-Nieto, L., Fernandez-Navarro, F., and Carbonero- ´ Ruz, M., An experimental study on diversification in portfolio optimization, Expert Systems with Applications, 2021, 181, P.0957–4174.

Doi: 10.1016/j.eswa.2021.115203.

 

[19] Bolos, M. I., Bradea, I. A., and Delcea, C., Optimization of financial asset neutrosophic portfolios, Mathematics, 2021, 9(11), P.1162. Doi:10.3390/math9111162.

 

[20] Markowitz, H., Portfolio selection, The journal of finance, 1952, 7(1), P.77-91. Doi: 10.2307/2975974.

 

[21] Ramaswamy, S., Portfolio Selection Using Fuzzy Decision Theory, Working Paper of Bank for International Settlements, 1998, 59.

 

[22] Rudin, W., Real and complex analysis, India: Tata McGraw-Hill, 1987.

 

[23] Taheri, M., Familiarity with fuzzy set theory (Unpublished master’s thesis), University Jihad, Mashhad, 1996.

 

[24] Sini., Guo, Lean., Yu, Xiang., Li, Samarjit., Kar, Fuzzy multi-period portfolio selection with different investment horizons, European Journal of Operational Research, 1 November 2016, 254(3), P.1026-1035.

Doi: 10.1016/j.ejor.2016.04.055.

 

[25] Tanaka, H., Guo, P., Portfolio selection based on upper and lowe exponential possibility distributions, Eurpean Journal of Operational Research, 1999, 114(1), P.115–126. Doi:10.1016/S0377-2217(98)00033-2.

 

[26] Tanaka, H., Guo, P., Tu¨ rksen, I. B., Portfolio selection based on fuzzy probabilities and possibility distributions, Fuzzy Sets and Systems, 2000, 111(3), P.387-397. Doi:10.1016/S0165-0114(98)00041-4.

 

[27] Wang, S. Y., Zhu, S. S., On fuzzy portfolio selection problems, Fuzzy Optimization and Decision Making, 2002, 1(4) , P.361–377. Doi:10.1023/A:1020907229361.

 

[28] Watada, J., Fuzzy portfolio model for decision making in investment, In Y. Yoshida (Ed.), Dynamical aspects in fuzzy decision making, Physica verlag: Heidelberg. 2001, P.141-162. Doi:10.1007/978-3-7908-1817-8_7.

 

[29] Woodside-Oriakhi, M., Lucas, C., Beasley, J. E., Heuristic algorithms for the cardinality constrained efficient frontier, European JoEurnal of Operational Research, 2011, 213(3), P.538-550.

Doi: 10,1016/j.ejor.2011,03,030.

 

[30] Yang, Y., Cao, J., Xu, X., Hu, M., Gao, Y., A new nerual network for solving quadratic programming problems with equality and inequality constraints, Mathematices and Computers in Simulation, 2014, 101, P. 103-112. Doi: 10.1016/j.matcom.2014.02.006.

 

[31] Zadeh, L. A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems, Man and Cybernetics, 1973, 1, P.28-44. Doi: 10.1109/TSMC.1973.5408575.

 

[32] Zhang, W. G., Nie. Z. K., On possibilistic variance of fuzzy numbers, Lecture Notes in Artificial Intelligence, 2003, 2639, P.398–402. Doi: 10.1007/3-540-39205-X_66.

 

[33] Zhang, W. G., Wang, Y. L., Using fuzzy possibilistic mean and variance in portfolio selection model, Lecture Notes in Artificial Intelligence, 2005, 3801, P. 291–296. Doi:10.1007/11596448_42.

 

[34] Abbasian-Naghneh, S., Tehrani, R., Tamimi, M. The Effect of JCPOA on the Network Behavior Analysis of Tehran Stock Exchange Indexes. Advances in Mathematical Finance and Applications, 2021, 6(3), P. 465-477, Doi: 10.22034/amfa.2019.1873319.1258

 

[35] Zanjirdar, M. Overview of Portfolio Optimization Models. Advances in Mathematical Finance and Applications, 2020, 5(4), P. 419-435. Doi: 10.22034/amfa.2020.674941

[36] Zangenehmehr, P., Farajzadeh, A. On Solutions of Generalized Implicit Equilibrium Problems with Application in Game Theory. Advances in Mathematical Finance and Applications, 2022, 7(2), P. 391-404. Doi: 10.22034/amfa.2021.1935453.1617

 

[37] Izadikhah, M. DEA Approaches for Financial Evaluation - A Literature Review, Advances in Mathematical Finance and Applications, 2022, 7(1), P. 1-36, Doi: 10.22034/amfa.2021.1942092.1639

 

[38] Salehi, A., Mohammadi, S., Afshari, M., Impact of Institutional Ownership and Board Independence on the Relationship Between Excess Free Cash Flow and Earnings Management. Advances in Mathematical Finance and Applications, 2017, 2(3), P. 91-105. Doi: 10.22034/amfa.2017.533104

[39] Parsa, B., Sarraf, F., Financial Statement Comparability and the Expected Crash Risk of Stock Prices. Advances in Mathematical Finance and Applications, 2018, 3(3), P. 77-93. Doi: 10.22034/amfa.2018.544951

[40] Jokar, H., Shamsaddini, K., Daneshi, V., Investigating the Effect of Investors' Behavior and Management on the Stock Returns: Evidence from Iran. Advances in Mathematical Finance and Applications, 2018, 3(3), P. 41-52. Doi: 10.22034/amfa.2018.544948

[41] Rezaei, 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

[42] Agah, M., Malekpoor, H., Bagheri, A., Investigating the Effect of Financial Constraints and Different Levels of Agency Cost on Investment Efficiency. Advances in Mathematical Finance and Applications, 2017, 2(4), P. 31-47. Doi: 10.22034/amfa.2017.536264

[43] Karbasi Yazdi, H., Mohammadian, M., Effect of Profitability Indices on the Capital Structure of Listed Companies in Tehran Stock Exchange. Advances in Mathematical Finance and Applications, 2017, 2(3), P. 1-11. Doi: 10.22034/amfa.2017.533085

[44] Ahmadi, R., Kordloei, H., The Effect of Financial Distress on the Investment Behavior of Companies Listed on Tehran Stock Exchange. Advances in Mathematical Finance and Applications, 2018, 3(4), P. 17-28. Doi: 10.22034/amfa.2019.565459.1108