no. 2
Tangency portfolios in the LP solvable portfolio selection models
RAIRO - Operations Research - Recherche Opérationnelle, Tome 46 (2012) no. 2, pp. 149-158.

A risk measure in a portfolio selection problem is linear programming (LP) solvable, if it has a linear formulation when the asset returns are represented by discrete random variables, i.e., they are defined by their realizations under specified scenarios. The efficient frontier corresponding to an LP solvable model is a piecewise linear curve. In this paper we describe a method which realizes and produces a tangency portfolio as a by-product during the procedure of tracing out of the efficient frontier of risky assets in an LP solvable model, when our portfolio contains some risky assets and a riskless asset, using nonsmooth optimization methods. We show that the test of finding the tangency portfolio can be limited only for two portfolios. Also, we describe that how this method can be employed to trace out the efficient frontier corresponding to a portfolio selection problem in the presence of a riskless asset.

DOI : 10.1051/ro/2012012
Classification : 90C05, 90C29
Mots clés : linear programming, lp solvable portfolio selection models, subgradient, tangency portfolio, Aneja-Nair method 
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     title = {Tangency portfolios in the {LP} solvable portfolio selection models},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {149--158},
     publisher = {EDP-Sciences},
     volume = {46},
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     year = {2012},
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Keykhaei, Reza; Jahandideh, Mohamad Taghi. Tangency portfolios in the LP solvable portfolio selection models. RAIRO - Operations Research - Recherche Opérationnelle, Tome 46 (2012) no. 2, pp. 149-158. doi : 10.1051/ro/2012012. http://www.numdam.org/articles/10.1051/ro/2012012/

[1] Y.P. Aneja and K.P.K. Nair, Bicriteria transportation problem. Manage. Sci. 25 (1979) 73-78. | MR | Zbl

[2] M.S. Bazaraa, J.J. Jarvis and H.D. Sherali, Linear programming and network flows, 3rd edition. John Wiley & Sons, New York (2005). | MR | Zbl

[3] X.Q. Cai, K.L. Teo, X.Q. Yang, and X.Y. Zhou, Portfolio optimization under a minimax rule. Manage. Sci. 46 (2000) 957-972. | Zbl

[4] J.-B. Hiriart-Urruty and C. Lemaréchal. Convex analysis and minimization algorithms I. Springer, Berlin, Heidelberg, New York (1993). | MR

[5] H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manage. Sci. 37 (1991) 519-529.

[6] T. Lust and J. Teghem, Two-phase pareto local search for the biobjective traveling salesman problem. J. Heuristics 16 (2010) 475-510. | Zbl

[7] R. Mansini, W. Ogryczak and M.G. Speranza, On LP solvable models for portfolio selection. Informatica 14 (2003) 37-62. | MR | Zbl

[8] H.M. Markowitz, Portfolio selection. J. Financ. 7 (1952) 77-91.

[9] R.T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk. J. Risk 2 (2000) 21-41. | Zbl

[10] W.F. Sharpe, The Sharpe ratio. J. Portfolio Manage. Fall (1994) 49-58.

[11] K.L. Teo and X.O. Yang, Portfolio selection problem with minimax type risk function. Ann. Oper. Res. 101 (2001) 333-349. | MR | Zbl

[12] R.H. Tütüncü, A note on calculating the optimal risky portfolio. Finance Stochastics 5 (2001) 413-417. | MR | Zbl

[13] S. Yitzhaki, Stochastic dominance, mean variance, and Ginis mean difference. Amer. Econ. Rev. 72 (1982) 178-185.

[14] M.R. Young, A minimax portfolio selection rule with linear programming solution. Manage. Sci. 44 (1998) 673-683. | Zbl

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