Soft Computing

, Volume 23, Issue 24, pp 13309–13320 | Cite as

Random credibilitic portfolio selection problem with different convex transaction costs

  • Peng ZhangEmail author
Methodologies and Application


Most of the portfolio optimization problems are devoted to either stochastic model or fuzzy one. However, practical portfolio selection problems often involve the mixture of the stochastic returns with fuzzy information. In this paper, we propose a new mean variance random credibilitic portfolio selection problem with different convex transaction costs, i.e., linear function, non-smooth convex function, smooth convex function. In this proposed model, we assume that the returns of assets obey the trapezoidal-type credibilitic distributions, and the risks obey the stochastic distributions. Based on the random credibilitic theories, these models are transformed into crisp convex programming problems. To find the optimal solution, we, respectively, present a pivoting algorithm, a branch-and-bound algorithm, and a sequence quadratic programming algorithm to solve these models. Furthermore, we offer numerical experiments of different forms of convex transaction costs to illustrate the effectiveness of the proposed model and approach.


Mean variance portfolio optimization model Random credibilitic variable Convex transaction costs A pivoting algorithm Sequence quadratic programming 



This research was supported by the National Natural Science Foundation of China (Nos. 71271161).

Compliance with ethical standards

Conflict of interest

Peng Zhang declares that he/she has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


  1. Al Janabi MAM, Hernandez JA, Berger T, Nguyen DK (2017) Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios. Eur J Oper Res 259:1121–1131MathSciNetCrossRefGoogle Scholar
  2. Arnott RD, Wagner WH (1990) The measurement and control of trading costs. Financ Anal J 6:73–80CrossRefGoogle Scholar
  3. Bertsimas D, Pachamanova D (2008) Robust multiperiod portfolio management in the presence of transaction costs. Comput Oper Res 35:3–17MathSciNetCrossRefGoogle Scholar
  4. Deng X, Zhao J, Li Z (2018) Sensitivity analysis of the fuzzy mean-entropy portfolio model with transaction costs based on credibility theory. Int J Fuzzy Syst 20(1):209–218MathSciNetCrossRefGoogle Scholar
  5. Dutta S, Biswal MP, Acharya S, Mishraa R (2018) Fuzzy stochastic price scenario based portfolio selection and its application to BSE using genetic algorithm. Appl Soft Comput 62:867–891CrossRefGoogle Scholar
  6. Gao J, Li D (2013) Optimal cardinality constrained portfolio selection. Oper Res 61(3):745–761MathSciNetCrossRefGoogle Scholar
  7. Gülpınar N, Rustem B, Settergren R (2003) Multistage stochastic mean-variance portfolio analysis with transaction cost. Innov Financ Econ Netw 3:46–63Google Scholar
  8. Hasuike T, Katagiri H, Ishii H (2009) Portfolio selection problems with random fuzzy variable returns. Fuzzy Sets Syst 160:2579–2596MathSciNetCrossRefGoogle Scholar
  9. Huang X (2007a) Two new models for portfolio selection with stochastic returns taking fuzzy information. Eur J Oper Res 180:396–405MathSciNetCrossRefGoogle Scholar
  10. Huang X (2007b) A new perspective for optimal portfolio selection with random fuzzy returns. Inf Sci 177:5404–5414MathSciNetCrossRefGoogle Scholar
  11. Jalota H, Thakur M, Mittalb G (2017) A credibilistic decision support system for portfolio optimization. Appl Soft Comput 59:512–528CrossRefGoogle Scholar
  12. Kar MB, Kar S, Guo S, Li X, Majumder S (2018) A new bi-objective fuzzy portfolio selection model and its solution through evolutionary algorithms. Soft Comput. CrossRefzbMATHGoogle Scholar
  13. Liagkouras K, Metaxiotis K (2017) A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem. Ann Oper Res. CrossRefzbMATHGoogle Scholar
  14. Liu B (2002a) Theory and practice of uncertain programming. Physica Verlag, HeidelbergCrossRefGoogle Scholar
  15. Liu B (2002b) Random fuzzy dependent-chance programming and its hybrid intelligent algorithm. Inf Sci 141:259–271CrossRefGoogle Scholar
  16. Liu Y, Tang W, Li X (2011) Random fuzzy shock models and bivariate random fuzzy exponential distribution. Appl Math Model 35:2408–2418MathSciNetCrossRefGoogle Scholar
  17. Macedo LL, Godinho P, Alves MJ (2017) Mean-semivariance portfolio optimization with multiobjective evolutionary algorithms and technical analysis rules. Expert Syst Appl 79:33–43CrossRefGoogle Scholar
  18. Markowitz H (1952) Portfolio selection. J Financ 7(1):77–91Google Scholar
  19. Mehlawat MK, Gupta P (2014) Fuzzy chance-constrained multiobjective portfolio selection model. IEEE Trans Fuzzy Syst 22(3):653–671CrossRefGoogle Scholar
  20. Qin Z (2017) Random fuzzy mean-absolute deviation models for portfolio optimization problem with hybrid uncertainty. Appl Soft Comput 56:597–603CrossRefGoogle Scholar
  21. Qin Z, Li X, Ji X (2009) Portfolio selection based on fuzzy cross-entropy. J Comput Appl Math 228:139–149MathSciNetCrossRefGoogle Scholar
  22. Vercher E, Bermudez J, Segura J (2007) Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets Syst 158:769–782MathSciNetCrossRefGoogle Scholar
  23. Wang B, Li Y, Watada J (2017) Multi-period portfolio selection with dynamic risk/expected return level under fuzzy random uncertainty. Inf Sci 385–386:1–18Google Scholar
  24. Yoshimoto A (1996) The mean–variance approach to portfolio optimization subject to transaction costs. J Oper Res Soc Japan 39:99–117MathSciNetzbMATHGoogle Scholar
  25. Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28MathSciNetCrossRefGoogle Scholar
  26. Zhang P (2016) An interval mean-average absolute deviation model for multiperiod portfolio selection with risk control and cardinality constraints. Soft Comput 15(1):63–76Google Scholar
  27. Zhang P (2017) Multiperiod mean semi- absolute deviation interval portfolio selection with entropy constraints. J Ind Manag Optim 13(3):1169–1187MathSciNetzbMATHGoogle Scholar
  28. Zhang P, Zhang W (2014) Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints. Fuzzy Sets Syst 255:74–91MathSciNetCrossRefGoogle Scholar
  29. Zhang W, Zhang X, Xiao W (2009) Portfolio selection under possibilistic mean–variance utility and a SMO algorithm. Eur J Oper Res 197:693–700CrossRefGoogle Scholar
  30. Zhang X, Zhang W, Xu W, Xiao W (2010) Possibilistic approaches to portfolio selection problem with general transaction costs and a CLPSO algorithm. Comput Econ 36:191–200CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Economics and ManagementSouth China Normal UniversityGuangzhouPeople’s Republic of China

Personalised recommendations