International Journal of Nonlinear Analysis and Applications

Designing a multi-period credit portfolio optimization model a nonlinear multi-objective fuzzy mathematical modeling approach (Case study: Ansar banks affiliated to Sepah Bank)

Document Type : Research Paper

Authors

1 Department of Financial Engineering, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

2 Department of Financial Management, Alzahra University, Tehran, Iran

3 Department of Accounting, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

Abstract

This study aims to design a multi-period credit portfolio optimization model with a nonlinear multi-objective fuzzy mathematical modeling approach. In terms of data collection, this study is a descriptive-survey research and in terms of the nature and purpose of the research, it is an applied one. The statistical population of the research includes all facility files of the last 10 years as well as the statements of financial position of Ansar Bank branches affiliated with Sepah Bank, selected by census method. The risk criteria used in the models include Average Value at Risk (AVaR), Conditional Value at Risk (CVAR) and Semi-Entropy. First, having reviewed the research literature, the objectives and indices of the portfolio optimization issue were investigated based on the practical character of this issue and the main indices were selected. Then, each of the objectives and constraints were specified in a state of uncertainty and ambiguity, based on the principles of fuzzy credibility theory, for a state in which the expected rate of stock return is a triangular fuzzy number. Finally, three multi-objective fuzzy models were designed based on the selected criteria. Research models were implemented using MOPSO algorithm. The software used in conducting the research was MATLAB software. The results indicated that the CVAR model performed better than the other two models, i.e. AVAR and Semi-Entropy, in evaluating optimal portfolios.

Keywords

[1] A. Arabmazar and P. Ruintan, Determinants of credit risk among bank clients a case study; Agricultural Bank of Iran, J. Iran. Econ. Ess. 3(6) (2006) 46–82.
[2] H. Asgharpur, F. Fallahi, N. Sanoubar and A. Rezazadeh, Stock optimal portfolio selection in a VaR framework: comparison the MS-GARCH and Bootstrapping methods, J. Econ. Mod. Res. 5(17) (2014) 87–122.
[3] Gh. Askarzadeh, Mathematical modeling to determine the optimal portfolio of lending facilities in financial and credit institutions, Andishe Sadegh Quart. 23 (2006) 107–130.
[4] A. Charnes and W.W. Cooper, Chance-constrained programming, Manag. Sci. 6(1) (1959) 73–79.
[5] M. Clerc and J. Kennedy, The particle swarm-explosion, stability, and convergence in a multidimensional complex space, IEEE Trans. Evol. Comput. 6(1) (2002) 58–73.
[6] G. Cornuejols and R. T¨ut¨unc¨u, Optimization methods in finance, Cambridge, UK: Cambridge University Press,2007.
[7] G.B. Dantzig, Linear programming under uncertainty, Manag. Sci. 1(3-4) (1995) 197–206.
[8] F. Demirchi, Investment portfolio optimization using conditional value at risk (CVaR) criteria in Tehran stock exchange, Unpublished MA Thesis in Financial Management, Al-Zahra University, Faculty of Social and Economic Sciences, 2010.
[9] H. Didehkhani, A. Shiri Ghahi, K. Khalili Damghani and P. Saeedi, A comparative study of multi-objective multiperiod portfolio optimization models in a fuzzy credibility environment using different risk measures, Financ. Manag. Strat. 5(3) (2017) 1–26.
[10] H. Didehkhani, A. Shiri Ghehi, K. Khalili Damghani and P. Saeedi, Developing a fuzzy multi-objective model for multi-period portfolio optimization considering average value at risk, Finan. Engin. Portfolio Manag. 9(35) (2018) 131–151.
[11] N. Ebrahimi Herdoroodi and S.A. Hosseini Yakani, Comparative study of the length of investment period in selecting the optimal portfolio using conditional value at risk (CVaR) index, The First International Conference on Management and Accounting with Value Creation Approach, Fars Islamic Azad University Science and Research Branch, 2015.
[12] S.B. Ebrahimi, and A. Jirofti, Investigating of using fuzzy credibility theory for measuring value at risk, Quart. J. Quant. Econ. 13(3) (2016) 1–24.
[13] S. Fallahpour, F. Rezvani and M. Rahimi, Estimating conditional VaR using symmetric and non-symmetric autoregressive models in old and oil markets, Finan. Knowledge Secur. Anal. 8(26) (2015) 1–18.
[14] S. Fallahpour and M. Baghban, Application of Copula-CVaR in portfolio optimization and comparative with mean-CVaR, Quart. J. Econ. Res. Pol. 22(72) (2015) 155–172.
[15] X. Huang, What is Portfolio analysis?, In: portfolio analysis, studies in fuzziness and soft computing, Springer, Berlin, Heidelberg, 2010.
[16] M. Karimi, Portfolio optimization using VaR venture value model in Tehran stock exchange, MA Thesis in Business Management, Al-Zahra University, 2007.
[17] H. Katagiri, T. Uno, K. Kato, H. Tsuda and H. Tsubaki, Random fuzzy bilevel linear programming through possibility-based value at risk model, Int. J. Machine Learning and Cybernetics 5(2) (2014) 211–224.
[18] M. Kazemi Miyangaskari, K. Yakideh and M. Gholizadeh, Portfolio optimization (The application of value at risk model on cross efficiency, Finan. Manag. Strat. 5(2) (2017) 159-183.
[19] B. Liu and B. Liu, Theory and Practice of Uncertain Programming, Heidelberg, Germany: Physica-Verlag, 2002.
[20] B. Liu, A survey of credibility theory, Fuzzy Opt. Dec. Mak. 5(4) (2006) 387–408.
[21] Y. Liu and J. Gao, The independence of fuzzy variables in credibility theory and its applications, Int. J. Uncer. Fuzz. Knowledge-Based Syst. 15 (2007) 1–20.
[22] H. Mirzaie R. Nazarian and R. Bagheri, A review of factors affecting the credit risk of the bank’s legal clients (a case of Melli Bank of Iran), Trend (Trend Econ. Res.), 19(58) (2011) 67–98.
[23] A.M. Moussa, J.S. Kamdem and M. Terraza, Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns, Econ. Mod. 39 (2014) 247–256.
[24] J. Peng, Measuring fuzzy risk by credibilistic value at risk, 2008 3rd Int. Conf. Innovative Computing Information and Control, Dalian, China, pp. 270-270, doi: 10.1109/ICICIC.2008.351.
[25] J. Peng, Credibilistic value and average value at risk in fuzzy risk analysis, Fuzzy Inf. Engin. 3(1) (2011) 69–79.
[26] Z. PoorAhmadi and A. A. Najafi, Dynamic optimization of investment portfolio with respect to transaction costs, Finan. Engin. Secur. Manag. 6(22) (2015) 127–146.
[27] S. T. Rachev, S. V. Stoyanov and F. J. Fabozzi, Advanced stochastic models, risk assessment, and portfolio optimization: The ideal risk, uncertainty, and performance measures, John Wiley & Sons, 2008.
[28] R. T. Rockafellar, S. Uryasev and M. Zabarankin, Generalized deviations in risk analysis, Fin. Stoc. 10(1) (2006) 51-74.
[29] W. F. Sharpe, J. V. Bailey and G. J. Alexander, Investments, 6th Edition, Prentice-Hall, Englewood Cliffs, 1999.
[30] M. Talebi and N. Shirzadi, Credit risk: measurement and management, Samat Pub. Co., Tehran, 2011.
[31] I. Usta and Y. M. Kantar, Mean-variance-skewness-entropy measures: a multi-objective approach for portfolio selection, Entropy, 13(1) (2011) 117–133.
[32] F. Vafaei, S. Latafati and A. Omid, Using fuzzy mathematical programming to design portfolio optimization model (case study: Melli Bank Investment Company), Indust. Manag. 7(21) (2012) 1–9.
[33] S. Wang and J. Watada, Two-stage fuzzy stochastic programming with value-at-risk criteria, App. Soft Comput. 11(1) (2011) 1044–1056.
[34] D. Xu, and U. Kaymak, Value-at-risk estimation by using probabilistic fuzzy systems, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), (2008) 2109-2116.
[35] J. Zhou, X. Li, and W. Pedrycz, Mean-Semi-Entropy Models of Fuzzy Portfolio Selection, IEEE Trans. Fuzzy Syst. 24(6)  (2016) 1627–1636.
[36] R. Zhou, R. Cai and G. Tong, Applications of entropy in finance: a review, Entropy 15(11) (2013) 4909–4931.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 1261-1277
  • Receive Date: 11 December 2020
  • Revise Date: 05 March 2021
  • Accept Date: 15 March 2021