Journal of Fuzzy Extension and Applications

Quarterly Publication

About Journal

Aims and Scope

Open Access Policy

Editorial Staff

Related Links

Journal Forms

Journal Metrics

Financial Policies

Crossmark Policy

Complaints

News

FAQ

Open Special Issues

Propose a Special Issue

Publication Ethics

Journal Policies

Editorial Board

Peer Review Policies

Guide for Reviewers

Reviewers (2022)

Reviewers (2021)

Reviewers (2020)

Join Us As Reviewer

Current Issue

By Issue

By Author

By Subject

Author Index

Keyword Index

A novel mathematical approach for fuzzy multi-period multi-objective portfolio optimization problem under uncertain environment and practical constraints

Document Type : Research Paper

Authors

1 School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran.

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

3 Department of Industrial and Manufacturing Engineering, University of Wisconsin-Milwaukee, Milwaukee, USA.

4 Sheldon B. Lubar School of Business, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA.

Abstract

Investment Portfolio Optimization (IPO) is one of the most important problems in the financial area. Also, one of the most important features of financial markets is their embedded uncertainty. Thus, it is essential to propose a novel IPO model that can be employed in the presence of uncertain data. Accordingly, the main goal of this paper is to propose a novel Fuzzy Multi-Period Multi-Objective Portfolio Optimization (FMPMOPO) model that is capable to be used under data ambiguity and practical constraints including budget constraint, cardinality constraint, and bound constraint. It should be noted that three objectives including terminal wealth, risk, and liquidity as well as practical constraints are considered in proposed FMPMOPO model. Also, the alpha-cut method is employed to deal with fuzzy data. Finally, the proposed Fuzzy Multi-Period Wealth-Risk-Liquidity (FMPWRL) model is implemented in real-world case study from Tehran Stock Exchange (TSE). The experimental results show the applicability and efficacy of the proposed FMPWRL model for fuzzy multi-period multi-objective investment portfolio optimization problem under fuzzy environment.

Keywords

Main Subjects

References
  1. Roman, D., & Mitra, G. (2009). Portfolio selection models: a review and new directions. Wilmott journal: the international journal of innovative quantitative finance research, 1(2), 69-85.
  2. Kolm, P. N., Tütüncü, R., & Fabozzi, F. J. (2014). 60 years of portfolio optimization: practical challenges and current trends. European journal of operational research, 234(2), 356-371.
  3. Mansini, R., Ogryczak, W., & Speranza, M. G. (2014). Twenty years of linear programming based portfolio optimization. European journal of operational research, 234(2), 518-535.
  4. Mokhtar, M., Shuib, A., & Mohamad, D. (2014). Mathematical programming models for portfolio optimization problem: a review. International journal of social, management, economics and business engineering, 8(2), 443-450.
  5. Zhang, Y., Li, X., & Guo, S. (2018). Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature. Fuzzy optimization and decision making, 17(2), 125-158.
  6. Milhomem, D. A., & Dantas, M. J. P. (2020). Analysis of new approaches used in portfolio optimization: a systematic literature review. Production, 30, e20190144. https://doi.org/10.1590/0103-6513.20190144
  7. Markowitz, H. (1952). Portfolio selection. The journal of finance, 7(1), 77-91.
  8. Sharpe, W. F. (1963). A simplified model for portfolio analysis. Management science, 9(2), 277-293.
  9. Kim, J. H., Kim, W. C., & Fabozzi, F. J. (2018). Recent advancements in robust optimization for investment management. Annals of operations research, 266(1-2), 183-198.
  10. Peykani, P., Mohammadi, E., Jabbarzadeh, A., Rostamy-Malkhalifeh, M., & Pishvaee, M. S. (2020). A novel two-phase robust portfolio selection and optimization approach under uncertainty: a case study of Tehran stock exchange. Plos One, 15(10), e0239810. https://doi.org/10.1371/journal.pone.0239810
  11. Peykani, P., Namakshenas, M., Arabjazi, N., Shirazi, F., & Kavand, N. (2021). Optimistic and pessimistic fuzzy data envelopment analysis: empirical evidence from Tehran stock market. Fuzzy optimization and modeling journal, 3(2), 12-21.
  12. Yin, C., Perchet, R., & Soupé, F. (2021). A practical guide to robust portfolio optimization. Quantitative finance, 21(6), 911-928.
  13. Zhu, B., & Zhang, T. (2021). Long-Term wealth growth portfolio allocation under parameter uncertainty: a non-conservative robust approach. The North American journal of economics and finance, 57, 101432. https://doi.org/10.1016/j.najef.2021.101432
  14. Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy sets and systems, 1(1), 3-28.
  15. Peykani, P., Mohammadi, E., Pishvaee, M. S., Rostamy-Malkhalifeh, M., & Jabbarzadeh, A. (2018). A novel fuzzy data envelopment analysis based on robust possibilistic programming: possibility, necessity and credibility-based approaches. RAIRO-Operations research, 52(4-5), 1445-1463.
  16. Peykani, P., Mohammadi, E., Emrouznejad, A., Pishvaee, M. S., & Rostamy-Malkhalifeh, M. (2019). Fuzzy data envelopment analysis: an adjustable approach. Expert systems with applications, 136, 439-452.
  17. Goli, A., Zare, H. K., Tavakkoli‐Moghaddam, R., & Sadegheih, A. (2020). Multiobjective fuzzy mathematical model for a financially constrained closed‐loop supply chain with labor employment. Computational intelligence, 36(1), 4-34.
  18. Tirkolaee, E. B., Goli, A., & Weber, G. W. (2020). Fuzzy mathematical programming and self-adaptive artificial fish swarm algorithm for just-in-time energy-aware flow shop scheduling problem with outsourcing option. IEEE transactions on fuzzy systems, 28(11), 2772-2783.
  19. Peykani, P., Hosseinzadeh Lotfi, F., Sadjadi, S. J., Ebrahimnejad, A., & Mohammadi, E. (2021). Fuzzy chance-constrained data envelopment analysis: a structured literature review, current trends, and future directions. Fuzzy optimization and decision making, 1-65.
  20. Peykani, P., Mohammadi, E., & Emrouznejad, A. (2021). An adjustable fuzzy chance-constrained network dea approach with application to ranking investment firms. Expert systems with applications, 166, 113938. https://doi.org/10.1016/j.eswa.2020.113938
  21. Sadjadi, S. J., Seyedhosseini, S. M., & Hassanlou, K. (2011). Fuzzy multi period portfolio selection with different rates for borrowing and lending. Applied soft computing, 11(4), 3821-3826.
  22. Liu, Y. J., Zhang, W. G., & Xu, W. J. (2012). Fuzzy multi-period portfolio selection optimization models using multiple criteria. Automatica, 48(12), 3042-3053.
  23. Zhang, W. G., Liu, Y. J., & Xu, W. J. (2012). A possibilistic mean-semi variance-entropy model for multi-period portfolio selection with transaction costs. European journal of operational research, 222(2), 341-349.
  24. Zhang, X., Zhang, W., & Xiao, W. (2013). Multi-Period portfolio optimization under possibility measures. Economic modelling, 35, 401-408.
  25. Zhang, P., & Zhang, W. G. (2014). Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints. Fuzzy sets and systems, 255, 74-91.
  26. Zhang, W. G., Liu, Y. J., & Xu, W. J. (2014). A new fuzzy programming approach for multi-period portfolio optimization with return demand and risk control. Fuzzy sets and systems, 246, 107-126.
  27. Mehlawat, M. K. (2016). Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels. Information sciences, 345, 9-26.
  28. Wang, B., Li, Y., & Watada, J. (2017). Multi-Period portfolio selection with dynamic risk/expected-return level under fuzzy random uncertainty. Information sciences, 385, 1-18.
  29. Liu, Y. J., & Zhang, W. G. (2018). Multiperiod fuzzy portfolio selection optimization model based on possibility theory. International journal of information technology & decision making, 17(03), 941-968.
  30. Liagkouras, K., & Metaxiotis, K. (2018). Multi-Period mean–variance fuzzy portfolio optimization model with transaction costs. Engineering applications of artificial intelligence, 67, 260-269.
  31. Cao, J. L. (2019). Algorithm research based on multi period fuzzy portfolio optimization model. Cluster computing, 22(2), 3445-3452.
  32. Liu, Y. J., & Zhang, W. G. (2019). Possibilistic moment models for multi-period portfolio selection with fuzzy returns. Computational economics, 53(4), 1657-1686.
  33. Gupta, P., Mehlawat, M. K., Yadav, S., & Kumar, A. (2020). Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models. Soft computing, 24, 11931–11956.
  34. Gupta, P., Mehlawat, M. K., & Khan, A. Z. (2020). Multi-Period portfolio optimization using coherent fuzzy numbers in a credibilistic environment. Expert systems with applications, 167, 114135. https://doi.org/10.1016/j.eswa.2020.114135
  35. Zadeh, L. A. (1996). Fuzzy sets. Fuzzy sets, fuzzy logic, and fuzzy systems, 394-432.
  36. Xu, J., & Zhou, X. (2011). Fuzzy-Like multiple objective decision making. Berlin: Springer.
  37. Charnes, A., & Cooper, W. W. (1977). Goal programming and multiple objective optimizations. European journal of operational research, 1(1), 39-54.
  38. Zanakis, S. H., & Gupta, S. K. (1985). A categorized bibliographic survey of goal programming. Omega, 13(3), 211-222.
  39. Tamiz, M., Jones, D., & Romero, C. (1998). Goal programming for decision making: an overview of the current state-of-the-art. European journal of operational research, 111(3), 569-581.
  40. Mulvey, J. M., Vanderbei, R. J., & Zenios, S. A. (1995). Robust optimization of large-scale systems. Operations research, 43(2), 264-281.
  41. Yu, C. S., & Li, H. L. (2000). A robust optimization model for stochastic logistic problems. International journal of production economics, 64(1-3), 385-397.
  42. Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations research, 52(1), 35-53.
  43. Ben-Tal, A., El Ghaoui, L., & Nemirovski, A. (2009). Robust optimization. Princeton University Press.
  44. Bertsimas, D., Brown, D. B., & Caramanis, C. (2011). Theory and applications of robust optimization. SIAM review, 53(3), 464-501.
  45. Li, Z., Ding, R., & Floudas, C. A. (2011). A comparative theoretical and computational study on robust counterpart optimization: I. robust linear optimization and robust mixed integer linear optimization. Industrial & engineering chemistry research, 50(18), 10567-10603.
  46. Li, Z., Tang, Q., & Floudas, C. A. (2012). A comparative theoretical and computational study on robust counterpart optimization: II. Probabilistic guarantees on constraint satisfaction. Industrial & engineering chemistry research, 51(19), 6769-6788.
  47. Li, Z., & Floudas, C. A. (2014). A comparative theoretical and computational study on robust counterpart optimization: III. Improving the quality of robust solutions. Industrial & engineering chemistry research, 53(33), 13112-13124.
  48. Gabrel, V., Murat, C., & Thiele, A. (2014). Recent advances in robust optimization: an overview. European journal of operational research, 235(3), 471-483.
  49. Gorissen, B. L., Yanıkoğlu, İ., & Den Hertog, D. (2015). A practical guide to robust optimization. Omega, 53, 124-137.
  50. Peykani, P., Mohammadi, E., Farzipoor Saen, R., Sadjadi, S. J., & Rostamy-Malkhalifeh, M. (2020). Data envelopment analysis and robust optimization: a review. Expert systems, 37(4), e12534. https://doi.org/10.1111/exsy.12534
  51. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444.
  52. Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078-1092.
  53. Liu, J. S., Lu, L. Y., Lu, W. M., & Lin, B. J. (2013). A survey of dea applications. Omega, 41(5), 893-902.
  54. Liu, J. S., Lu, L. Y., & Lu, W. M. (2016). Research fronts in data envelopment analysis. Omega, 58, 33-45.
  55. Emrouznejad, A., & Yang, G. L. (2018). A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016. Socio-Economic planning sciences, 61, 4-8.
  56. Adam, L., & Branda, M. (2021). Risk-Aversion in data envelopment analysis models with diversification. Omega, 102, 102338. https://doi.org/10.1016/j.omega.2020.102338
  57. Amin, G. R., & Hajjami, M. (2021). Improving DEA cross-efficiency optimization in portfolio selection. Expert systems with applications, 168, 114280. https://doi.org/10.1016/j.eswa.2020.114280
  58. Gong, X., Yu, C., Min, L., & Ge, Z. (2021). Regret theory-based fuzzy multi-objective portfolio selection model involving DEA cross-efficiency and higher moments. Applied soft computing, 100, 106958. https://doi.org/10.1016/j.asoc.2020.106958
  59. Peykani, P., Farzipoor Saen, R., Seyed Esmaeili, F. S., & Gheidar-Kheljani, J. (2021). Window data envelopment analysis approach: a review and bibliometric analysis. Expert systems, e12721. https://doi.org/10.1111/exsy.12721
  60. Ren, T., Zhou, Z., & Xiao, H. (2021). Estimation of portfolio efficiency considering social responsibility: evidence from the multi-horizon diversification DEA. RAIRO-Operations research, 55(2), 611-637.
  61. Xiao, H., Ren, T., Zhou, Z., & Liu, W. (2021). Parameter uncertainty in estimation of portfolio efficiency: evidence from an interval diversification-consistent dea approach. Omega, 103, 102357. https://doi.org/10.1016/j.omega.2020.102357
  62. Zhou, Z., Gao, M., Xiao, H., Wang, R., & Liu, W. (2021). Big Data and portfolio optimization: a novel approach integrating DEA with multiple data sources. Omega, 104, 102479. https://doi.org/10.1016/j.omega.2021.102479
  63.  
Journal of Fuzzy Extension and Applications
Volume 2, Issue 3
September 2021
Pages 191-203
Files
Share
How to cite
Statistics