Table of Contents Author Guidelines Submit a Manuscript
Advances in Operations Research
Volume 2016, Article ID 7828071, 9 pages
http://dx.doi.org/10.1155/2016/7828071
Research Article

Usage of Cholesky Decomposition in order to Decrease the Nonlinear Complexities of Some Nonlinear and Diversification Models and Present a Model in Framework of Mean-Semivariance for Portfolio Performance Evaluation

1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received 22 October 2015; Revised 12 February 2016; Accepted 14 February 2016

Academic Editor: Shey-Huei Sheu

Copyright © 2016 H. Siaby-Serajehlo 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

  1. Time Magazine, vol. 148, no. 16, 1996.
  2. H. Markowitz, “Portfolio selection,” The Journal of Finance, vol. 7, no. 1, pp. 77–91, 1952. View at Publisher · View at Google Scholar
  3. W. F. Sharpe, “Capital asset prices: a theory of market equilibrium under conditions of risk,” The Journal of Finance, vol. 19, no. 3, pp. 425–442, 1964. View at Publisher · View at Google Scholar
  4. M. J. Lynge and J. K. Zumwalt, “An empirical study of the interest rate sensitivity of commercial bank returns: a multi-index approach,” Journal of Financial and Quantitative Analysis, vol. 15, no. 3, pp. 731–742, 1980. View at Publisher · View at Google Scholar
  5. M. R. Morey and R. C. Morey, “Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking,” Omega, vol. 27, no. 2, pp. 241–258, 1999. View at Publisher · View at Google Scholar · View at Scopus
  6. W. Briec, K. Kerstens, and J. B. Lesourd, “Single-period Markowitz portfolio selection, performance gauging, and duality: a variation on the Luenberger shortage function,” Journal of Optimization Theory and Applications, vol. 120, no. 1, pp. 1–27, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. A. Kane, “Skewness preference and portfolio choice,” The Journal of Financial and Quantitative Analysis, vol. 17, no. 1, pp. 15–25, 1982. View at Publisher · View at Google Scholar
  8. F. D. Arditti, “Skewness and investors' decisions: a reply,” The Journal of Financial and Quantitative Analysis, vol. 10, no. 1, pp. 173–176, 1975. View at Publisher · View at Google Scholar
  9. Y. K. Ho and Y. L. Cheung, “Behavior of intra-daily stock return on an Asian emerging market-Hong Kong,” Applied Economics, vol. 23, no. 5, pp. 957–966, 1991. View at Publisher · View at Google Scholar
  10. T. Joro and P. Na, “Portfolio performance evaluation in a mean–variance–skewness framework,” European Journal of Operational Research, vol. 175, no. 1, pp. 446–461, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. P. B. Hazell, “A linear alternative to quadratic and semivariance programming for farm planning under uncertainty,” American Journal of Agricultural Economics, vol. 53, no. 1, pp. 53–62, 1971. View at Publisher · View at Google Scholar
  12. J. Estrada, “Mean-semivariance behavior: downside risk and capital asset pricing,” International Review of Economics & Finance, vol. 16, no. 2, pp. 169–185, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, John Wiley & Sons, New York, NY, USA, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. C. Buchanan, Techniques for solving nonlinear programming problems with emphasis on interior point methods and optimal control problems [Master of Philosophy], Department of Mathematics and Statistics, University of Edinburgh, 2008.
  15. K. E. Atkinson, An Introduction to Numerical Analysis, John Wiley & Sons, New York, NY, USA, 2008.
  16. M. W. Davis, “Production of conditional simulations via the LU triangular decomposition of the covariance matrix,” Mathematical Geology, vol. 19, no. 2, pp. 91–98, 1987. View at Publisher · View at Google Scholar · View at Scopus
  17. D. M. Hawkins and W. J. R. Eplett, “The Cholesky factorization of the inverse correlation or covariance matrix in multiple regression,” Technometrics, vol. 24, no. 3, pp. 191–198, 1982. View at Publisher · View at Google Scholar · View at Scopus
  18. C. Hassold, The Valuation of Multivariate Options, diplom. De, 2004.
  19. D. Duffie and J. Pan, “An overview of value at risk,” The Journal of Derivatives, vol. 4, no. 3, pp. 7–49, 1997. View at Publisher · View at Google Scholar
  20. C. Genest and A.-C. Favre, “Everything you always wanted to know about copula modeling but were afraid to ask,” Journal of Hydrologic Engineering, vol. 12, no. 4, pp. 347–368, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. B. Mandelbrot, “The variation of certain speculative prices,” Journal of Business, vol. 36, no. 4, pp. 394–419, 1963. View at Publisher · View at Google Scholar
  22. I. Popova, E. Popova, D. Morton, and J. Yau, “Optimal hedge fund allocation with asymmetric preferences and distributions,” SSRN, 900012, 2006.
  23. R. J. Davies, H. M. Kat, and S. Lu, “Fund of hedge funds portfolio selection: a multiple-objective approach,” Journal of Derivatives & Hedge Funds, vol. 15, no. 2, pp. 91–115, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. L. T. DeCarlo, “On the meaning and use of kurtosis,” Psychological Methods, vol. 2, no. 3, pp. 292–307, 1997. View at Publisher · View at Google Scholar · View at Scopus
  25. W. Briec, K. Kerstens, and O. Jokung, “Mean-variance-skewness portfolio performance gauging: a general shortage function and dual approach,” Management Science, vol. 53, no. 1, pp. 135–149, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. A. S. Taylan and H. Tatlıdil, “Portfolio optimization with short function and higher order moments: an application in ISE-30,” in Proceedings of the 24th Mini EURO Conference, Continuous Optimization and Information-Based Technologies in the Financial Sector (MEC EurOPT '10), İzmir, Turkey, June 2010.
  27. K. K. Lai, L. Yu, and S. Wang, “Mean-variance-skewness-kurtosis-based portfolio optimization,” in Proceedings of the 1st International Multi-Symposiums on Computer and Computational Sciences (IMSCCS '06), vol. 2, pp. 292–297, Hanzhou, China, April 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. B. Aracioglu, F. Demircan, and H. Soyuer, “Mean-variance-skewness-kurtosis approach to portfolio optimization: an application in Istanbul stock exchange, IMKB Uygulamasi,” Ege Akademik Bakis, vol. 11, pp. 9–17, 2011. View at Google Scholar