Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 9461021, 13 pages
http://dx.doi.org/10.1155/2016/9461021
Research Article
Modeling Portfolio Optimization Problem by Probability-Credibility Equilibrium Risk Criterion
Key Laboratory in Machine Learning & Computational Intelligence, College of Mathematics & Information Science, Hebei University, Baoding, Hebei 071002, China
Received 3 December 2015; Accepted 15 February 2016
Academic Editor: Kishin Sadarangani
Copyright © 2016 Ye Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- H. Markowitz, “Portfolio selection,” Journal of Finance, vol. 7, no. 1, pp. 77–91, 1952. View at Publisher · View at Google Scholar
- H. M. Markowitz, Portfolio Selection: Efficient Diversification of Investments, John Wiley & Sons, 1959. View at MathSciNet
- H. Konno and H. Yamazaki, “Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market,” Management Science, vol. 37, no. 5, pp. 519–531, 1991. View at Publisher · View at Google Scholar
- Y. Simaan, “Estimation risk in portfolio selection: the mean variance model versus the mean absolute deviation model,” Management Science, vol. 43, no. 10, pp. 1437–1446, 1997. View at Publisher · View at Google Scholar · View at Scopus
- P. Jorion, Value at Risk: The New Benchmark for Controlling Market Risk, Irwin Professional Publishing, Willowbrook, Ill, USA, 1997.
- S. Y. Wang and Y. S. Xia, Portfolio Selection and Asset Pricing, Springer, Berlin, Germany, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
- L. Yu, S. Wang, and K. K. Lai, “Neural network-based mean-variance-skewness model for portfolio selection,” Computers and Operations Research, vol. 35, no. 1, pp. 34–46, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- R. T. Rockafellar and S. Uryasev, “Conditional value-at-risk for general loss distributions,” Journal of Banking and Finance, vol. 26, no. 7, pp. 1443–1471, 2002. View at Publisher · View at Google Scholar · View at Scopus
- A. Ang, D. Papanikolaou, and M. M. Westerfield, “Portfolio choice with illiquid assets,” Management Science, vol. 60, no. 11, pp. 2737–2761, 2014. View at Publisher · View at Google Scholar · View at Scopus
- Y. Shen, X. Zhang, and T. K. Siu, “Mean-variance portfolio selection under a constant elasticity of variance model,” Operations Research Letters, vol. 42, no. 5, pp. 337–342, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- L. A. Zadeh, “Fuzzy sets,” Information and Computation, vol. 8, pp. 338–353, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems, vol. 1, no. 1, pp. 3–28, 1978. View at Google Scholar · View at MathSciNet
- J. Watada, “Fuzzy portfolio selection and its application to decision making,” Tatra Mountains Mathematical Publication, vol. 13, pp. 219–248, 1997. View at Google Scholar
- H. Tanaka and P. Guo, “Portfolio selection based on upper and lower exponential possibility distributions,” European Journal of Operational Research, vol. 114, no. 1, pp. 115–126, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- M. Inuiguchi and J. Ramík, “Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem,” Fuzzy Sets and Systems, vol. 111, no. 1, pp. 3–28, 2000. View at Publisher · View at Google Scholar
- C. Carlsson, R. Fullér, and P. Majlender, “A possibilistic approach to selecting portfolios with highest utility score,” Fuzzy Sets and Systems, vol. 131, no. 1, pp. 13–21, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- Y. Fang, K. K. Lai, and S.-Y. Wang, “Portfolio rebalancing model with transaction costs based on fuzzy decision theory,” European Journal of Operational Research, vol. 175, no. 2, pp. 879–893, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- Y. Chen, Y. Liu, and J. Chen, “Fuzzy portfolio selection problems based on credibility theory,” in Advances in Machine Learning and Cybernetics, vol. 3930 of Lecture Notes in Computer Science, pp. 377–386, Springer, 2006. View at Publisher · View at Google Scholar
- X. Zhang, W.-G. Zhang, and R. Cai, “Portfolio adjusting optimization under credibility measures,” Journal of Computational and Applied Mathematics, vol. 234, no. 5, pp. 1458–1465, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- Z. Qin, X. Li, and X. Ji, “Portfolio selection based on fuzzy cross-entropy,” Journal of Computational and Applied Mathematics, vol. 228, no. 1, pp. 139–149, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- H. Dastkhan, N. S. Gharneh, and H. Golmakani, “A linguistic-based portfolio selection model using weighted max-min operator and hybrid genetic algorithm,” Expert Systems with Applications, vol. 38, no. 9, pp. 11735–11743, 2011. View at Publisher · View at Google Scholar · View at Scopus
- X.-L. Wu and Y.-K. Liu, “Optimizing fuzzy portfolio selection problems by parametric quadratic programming,” Fuzzy Optimization and Decision Making, vol. 11, no. 4, pp. 411–449, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- Y. Chen, Y. Liu, and X. Wu, “A new risk criterion in fuzzy environment and its application,” Applied Mathematical Modelling, vol. 36, no. 7, pp. 3007–3028, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- J. S. Kamdem, C. T. Deffo, and L. A. Fono, “Moments and semi-moments for fuzzy portfolio selection,” Insurance: Mathematics & Economics, vol. 51, no. 3, pp. 517–530, 2012. View at Publisher · View at Google Scholar · View at Scopus
- M. K. Mehlawat and P. Gupta, “Fuzzy chance-constrained multiobjective portfolio selection model,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 3, pp. 653–671, 2014. View at Publisher · View at Google Scholar · View at Scopus
- X. Deng and R. Li, “Gradually tolerant constraint method for fuzzy portfolio based on possibility theory,” Information Sciences, vol. 259, pp. 16–24, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- T. Li, W. Zhang, and W. Xu, “A fuzzy portfolio selection model with background risk,” Applied Mathematics and Computation, vol. 256, pp. 505–513, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- E. Vercher and J. D. Bermúdez, “Portfolio optimization using a credibility mean-absolute semi-deviation model,” Expert Systems with Applications, vol. 42, no. 20, pp. 7121–7131, 2015. View at Publisher · View at Google Scholar
- Y. Chen and Y. Wang, “Two-stage fuzzy portfolio selection problem with transaction costs,” Mathematical Problems in Engineering, vol. 2015, Article ID 675157, 12 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
- X. Huang, “Two new models for portfolio selection with stochastic returns taking fuzzy information,” European Journal of Operational Research, vol. 180, no. 1, pp. 396–405, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- Y.-K. Liu and B. Liu, “Random fuzzy programming with chance measures defined by fuzzy integrals,” Mathematical and Computer Modelling, vol. 36, no. 4-5, pp. 509–524, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
- B. Liu, Theory and Practice of Uncertain Programming, Physica, Heidelberg, Germany, 2002.
- Y.-K. Liu and B. Liu, “Expected value operator of random fuzzy variable and random fuzzy expected value models,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 11, no. 2, pp. 195–215, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
- B. Liu and Y.-K. Liu, “Expected value of fuzzy variable and fuzzy expected value models,” IEEE Transactions on Fuzzy Systems, vol. 10, no. 4, pp. 445–450, 2002. View at Publisher · View at Google Scholar · View at Scopus
- Y.-K. Liu and J. Gao, “The independence of fuzzy variables with applications to fuzzy random optimization,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 15, pp. 1–20, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
- Y. Liu and Y. Wang, “Equilibrium mean value of random fuzzy variable and its convergence properties,” Journal of Uncertain Systems, vol. 7, no. 4, pp. 243–253, 2013. View at Google Scholar · View at Scopus