Advertisement

Possibilistic Moment Models for Multi-period Portfolio Selection with Fuzzy Returns

  • Yong-Jun Liu
  • Wei-Guo Zhang
Article
  • 75 Downloads

Abstract

The aim of this paper is to investigate the effects of higher moments on multi-period portfolio selection with fuzzy returns. This paper gives the definitions of possibilistic mean and variance about the product of multiple fuzzy numbers. Based on these definitions, three multi-period fuzzy portfolio optimization models are proposed. The proposed models aim to maximize terminal wealth and minimize terminal risk by taking into account some realistic constraints including higher moments, budget constraint, round-lot constraint, cardinality constraint and bound constraint. To ensure the selection of the best solutions, a novel fuzzy programming approach-based self-adaptive differential evolution algorithm is designed to solve the proposed models. A numerical example is given to demonstrate the application of the proposed models. Computational results show that the designed algorithm is effective for solving complex portfolio selection model with realistic constraints.

Keywords

Multi-period portfolio selection Fuzzy set Higher moments Differential evolution 

Notes

Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 71501076 and 71720107002), the Natural Science Foundation of Guangdong Province of China (No. 2017A030312001), the Fundamental Research Funds for the Central Universities (No. 2017ZD102) and Guangzhou Financial Services Innovation and Risk Management Research Base.

References

  1. Ammar, E., & Khalifa, H. A. (2003). Fuzzy portfolio optimization: A quadratic programming approach. Chaos, Solitons & Fractals, 18(5), 1045–1054.CrossRefGoogle Scholar
  2. Ballestero, E., Günther, M., Pla-Santamaria, D., & Stummer, C. (2007). Portfolio selection under strict uncertainty: A multi-criteria methodology and its application to the Frankfurt and Vienna stock exchanges. European Journal of Operational Research, 181(3), 1476–1487.CrossRefGoogle Scholar
  3. Bellman, R., & Zadeh, L. A. (1970). Decision making in a fuzzy environment. Management Science, 17(4), 141–164.CrossRefGoogle Scholar
  4. Briec, W., Kerstens, K., & Jokung, O. (2007). Mean–variance–skewness portfolio performance gauging: A general shortage function and dual approach. Management Science, 53(1), 135–149.CrossRefGoogle Scholar
  5. Carli, R., Dotoli, M., Pellegrino, R., & Ranieri, L. (2017). A decision making technique to optimize a buildings’ stock energy efficiency. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47(5), 794–807.CrossRefGoogle Scholar
  6. Carlsson, C., & Fullér, R. (2001). On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems, 122(2), 315–326.CrossRefGoogle Scholar
  7. Chen, W. (2015). Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica A, 429, 125–139.CrossRefGoogle Scholar
  8. Chen, W., & Tan, S. (2009). On the possibilistic mean value and variance of multiplication of fuzzy numbers. Journal of Computational and Applied Mathematics, 232(2), 327–334.CrossRefGoogle Scholar
  9. Cheng, C. B. (2004). Group opinion aggregation based on a grading process: A method for constructing triangular fuzzy numbers. Computers & Mathematics with Applications, 48(10–11), 1619–1632.CrossRefGoogle Scholar
  10. Devi, B. B., & Sarma, V. V. S. (1985). Estimation of fuzzy memberships from histograms. Information Sciences, 35(1), 43–59.CrossRefGoogle Scholar
  11. Díaz, A., González, M. D. L. O., Navarro, E., & Skinner, F. S. (2009). An evaluation of contingent immunization. Journal of Banking & Finance, 33(10), 1874–1883.CrossRefGoogle Scholar
  12. DiTraglia, F. J., & Gerlach, J. R. (2013). Portfolio selection: An extreme value approach. Journal of Banking & Finance, 37(2), 305–323.CrossRefGoogle Scholar
  13. Dubios, D., & Prade, H. (1980). Fuzzy sets and system: Theory and application. New York: Academic Press.Google Scholar
  14. Fang, H., & Lai, T. Y. (1997). Go-kurtosis and capital asset pricing. Financial Review, 32(2), 293–307.CrossRefGoogle Scholar
  15. Ge, B., Hipel, K. W., Fang, L., Yang, K., & Chen, Y. (2014). An interactive portfolio decision analysis approach for system-of-systems architecting using the graph model for conflict resolution. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 44(10), 1328–1346.CrossRefGoogle Scholar
  16. Gong, C., Xu, C., Wang, J. (2017). An efficient adaptive real coded genetic algorithm to solve the portfolio choice problem under cumulative prospect theory. Computational Economics, 1C26 (in press).Google Scholar
  17. Ghosh, A., Das, S., Chowdhury, A., & Giri, R. (2011). An improved differential evolution algorithm with fitness-based adaptation of the control parameters. Information Sciences, 181(18), 3749–3765.CrossRefGoogle Scholar
  18. Guo, S., Yu, L., Li, X., & Kar, S. (2016). Fuzzy multi-period portfolio selection with different investment horizons. European Journal of Operational Research, 254(3), 1026–1035.CrossRefGoogle Scholar
  19. Gupta, P., Mehlawat, M. K., & Saxena, A. (2008). Asset portfolio optimization using fuzzy mathematical programming. Information Sciences, 178(6), 1734–1755.CrossRefGoogle Scholar
  20. Hjalmarsson, E., & Manchev, P. (2012). Characteristic-based mean–variance portfolio choice. Journal of Banking & Finance, 36(5), 1392–1401.CrossRefGoogle Scholar
  21. Jalota, H., Thakur, M., & Mittal, G. (2017). Modelling and constructing membership function for uncertain portfolio parameters: A credibilistic framework. Expert Systems with Applications, 71, 40–56.CrossRefGoogle Scholar
  22. Kim, T. (2015). Does individual-stock skewness/coskewness reflect portfolio risk? Finance Research Letters, 15, 167–174.CrossRefGoogle Scholar
  23. Kumar, R., & Bhattacharya, S. (2012). Cooperative search using agents for cardinality constrained portfolio selection problem. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 42(6), 1510–1518.CrossRefGoogle Scholar
  24. Leung, M. T., Daouk, H., & Chen, A. S. (2001). Using investment portfolio returns to combine forecasts: A multi-objective approach. European Journal of Operational Research, 134(1), 84–102.CrossRefGoogle Scholar
  25. Li, X., Guo, S., & Yu, L. (2015). Skewness of Fuzzy Numbers and Its Applications in Portfolio Selection. IEEE Transactions on Fuzzy Systems, 23(6), 2135–2143.CrossRefGoogle Scholar
  26. Li, J., Liu, G., Yan, C., & Jiang, C. (2017). Robust learning to rank based on portfolio theory and AMOSA algorithm. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 77(6), 1007–1018.CrossRefGoogle Scholar
  27. Li, X., Qin, Z. F., & Kar, S. (2010). Mean–variance–skewness model for portfolio selection with fuzzy returns. European Journal of Operational Research, 202(1), 239–247.CrossRefGoogle Scholar
  28. Liu, L., Shenoy, C., & Shenoy, P. P. (2006). Knowledge representation and integration for portfolio evaluation using linear belief functions. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 36(4), 774–785.CrossRefGoogle Scholar
  29. Liu, Y. J., & Zhang, W. G. (2013). Fuzzy portfolio optimization model under real constraints. Insurance: Mathematics and Economics, 53(3), 704–711.Google Scholar
  30. Mashayekhi, Z., & Omrani, H. (2016). An integrated multi-objective Markowitz-DEA cross-efficiency model with fuzzy returns for portfolio selection problem. Applied Soft Computing, 38, 1–9.CrossRefGoogle Scholar
  31. Mehlawat, M. K. (2016). Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels. Information Sciences, 345, 9–26.CrossRefGoogle Scholar
  32. Mohamed, A. W., & Sabry, H. Z. (2012). Constrained optimization based on modified differential evolution algorithm. Information Sciences, 194, 171–208.CrossRefGoogle Scholar
  33. Saborido, R., Ruiz, A. B., Bermúdez, J. D., Vercher, E., & Luque, M. (2016). Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection. Applied Soft Computing, 39, 48–63.CrossRefGoogle Scholar
  34. Saeidifar, A., & Pasha, E. (2009). The possibilistic moments of fuzzy numbers and their applications. Journal of Computational and Applied Mathematics, 223(2), 1028–1042.CrossRefGoogle Scholar
  35. Shen, Y. (2015). Mean–variance portfolio selection in a complete market with unbounded random coefficients. Automatica, 55, 165–175.CrossRefGoogle Scholar
  36. Storn, R., & Price, K. (1995). Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report TR-95-012. International Computer Science Institute, Berkeley, CA.Google Scholar
  37. Utz, S., Wimmer, M., Hirschberger, M., & Steuer, R. E. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491–498.CrossRefGoogle Scholar
  38. Wu, L. H., & Wang, Y. N. (2007). Self-adapting control parameters modified differential evolution for trajectory planning manipulator. Control Theory and Technology, 5(4), 365–373.CrossRefGoogle Scholar
  39. Yu, J. R., & Lee, W. Y. (2011). Portfolio rebalancing model using multiple criteria. European Journal of Operational Research, 209(2), 166–175.CrossRefGoogle Scholar
  40. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.CrossRefGoogle Scholar
  41. Zhang, W. G., Liu, Y. J., & Xu, W. J. (2012). A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs. European Journal of Operational Research, 222(2), 341–349.CrossRefGoogle Scholar
  42. Zhang, W. G., Xiao, W. L., & Xu, W. J. (2010a). A possibilistic portfolio adjusting model with new added assets. Economic Modelling, 27(1), 208–213.CrossRefGoogle Scholar
  43. Zhang, X. L., Zhang, W. G., Xu, W. J., & Xiao, W. L. (2010b). Possibilistic approaches to portfolio selection problem with general transaction costs and a CLPSO algorithm. Computational Economics, 36(3), 191–200.CrossRefGoogle Scholar
  44. Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45–55.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Business AdministrationSouth China University of TechnologyGuangzhouPeople’s Republic of China

Personalised recommendations