Portfolio optimization: a survey
Keywords:
Markowitz, portfolio optimization, absolute deviation, portfolio diversification, efficient frontier, Sharpe ratio, minimax model, integer variables, fuzzy expected returnAbstract
Optimization models play an increasingly role in financial decisions. This paper analyzes the portfolio optimization model which is the most important of them. We are discussing the mathematical models and modern optimization techniques for some classes of portfolio optimization problems more important criteria. Portfolio optimization problems are based on mean-variance models for returns and for riskneutral density estimation. The mathematical portfolio optimization problems are the quadratic or linear parametrical programming sometimes with integer variables.
References
- Markowitz H. Portfolio Selection. J. Finance. 1952. Vol. 7, No. 1. Р. 77–91. DOI: 10.1111/j.1540-6261.1952.tb01525.x.
- Sharpe W. Simplified model for portfolio analysis. Manag. Sci. 1963. Vol. 9, No. 2. P. 277–293.
- Markowitz H. Mean-variance analysis in portfolio choice and capital markets. Oxford : Blackwell Publishing, 1992.
- Tobin J. Liquidity preference as behavior towards risk. Rev. Econ. Stud. 1958. Vol. 25, No. 2. P. 65–86.
- Jana P., Roy T. K., Mazumber S. K. Multi-objective mean-variance-skewness model for portfolio optimization. AMO-Adv. Model. Optim. 2007. Vol. 9, No. 1. P. 181–193. 6. Konno H., Yamazaki H. Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manag. Sci. 1991. Vol. 37, No. 5. P. 519–531. DOI: https://doi.org/10.1287/mnsc.37.5.519.
- Feinstein C., Thapa M. A reformation of a mean-absolute deviation portfolio optimization model. Manag. Sci. 1993. No. 39. P. 1552–1553.
- Speranza M. Linear programming model for portfolio optimization. Finance. 1993. Vol. 14. P. 107–123.
- Young M. A Minimax, portfolio selection rule with linear programming solution. Manag. Sci. 1998. Vol. 44, No. 5. P. 673–683.
- Papahristodoulou C., Dotzauer E. Optimal portfolio using linear programming models. Y. Oper Res. Soc. 2004. No. 55. P. 1169–1177.
- Cai X., Teo K., Yang X., et al. Portfolio optimization under a minimax rule. Manag. Sci. 2000. No. 46. P. 957–972.
- Teo K., Yang X. Portfolio selection problem with minimax type risk function. Ann. Oper. Res. 2001. Vol. 101. P. 333–349. DOI: https://doi.org/10.1023/A:1010909632198.
- Sharpe W. The Sharpe ratio. J. Portfolio Manag. 1994. Vol. 21, No. 1. P. 49–58. DOI: https://doi.org/10.3905/jpm.1994.409501.
- Cornujeols G., Tutuncu R. Optimization methods in finance. Cambridge : Cambridge University Press, 2007.
- Jobst N., Horniman M., Lucas C., et al. Computational aspects of alternative portfolio selection models in the presence of dis crete asset choice costrains. Quant. Finance. 2001. Vol. 1, issue 5. P. 489–501. DOI: http://dx.doi.org/10.1088/1469-7688/1/5/301.
- Mansini R., Speranza M. Heuristic algorithms for the portfolio selection problem with minimum transaction lots. Eur. J. Oper. Res. 1999. Vol. 114, issue 2. P. 219 –233. DOI: https://doi.org/10.1016/S0377-2217(98)00252-5.
- Lai K., Wang S., Xu J., et al. A class of linear interval programming problems and its application to portfolio selection. IEEE Trans. on Fuzzy Syst. 2002. Vol. 10, No. 6. P. 698–704.
- Li D., Sun X., Wang S. Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection. Math. Finance. 2006. Vol. 16, No. 1. P. 83–101. 19. Dubois D., Prade H. Possibility theory. New York : Plenum Press, 1998.
- Bolshakova I., Kovalev M. Fuzzy numbers in financial analyses. The problems of forecast and state regulation of social and economic development : papers of 5th Int. sci. conf. (Minsk, 21–22 Oct., 2004). Minsk, 2004. P. 459 – 473.
- Bertsimas D., Darnell C., Soucy R. Portfolio construction through mixed-integer programming at Grantham, Moyo, Van Otterloo and Company. INTERFACES. 1999. Vol. 29, No. l. P. 49 – 66.
- Bolshakova I., Kovalev M., Girlich E. Portfolio optimization problems : a survey. Magdeburg, 2009. P. 1–19 (Preprint / Otto- von-Guericke University Magdeburg ; No. 6).
- Wolfram S. Mathematica. A system for doing mathematics by computer. 2nd ed. Redwood City (CA) : Addison-Wesley Publishing Company, 1991.
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