Volume 22, No 2, 2015, P. 5-16
UDC 519.17
S. E. Bukhtoyarov, V. A. Emelichev
On stability of solutions of a vector variant of one investment problem
Abstract:
The vector Boolean problem of portfolio optimization with extreme optimism criteria and Pareto optimality principle is considered. Upper and lower bounds of stability radius are given with an arbitrary Hölder metric in the space of investment projects and in the space of factors of projects economical efficiency and with the Chebyshev metric in the space of financial market states.
Bibliogr. 10.
Keywords: vector investment problem, extreme optimism criteria, Pareto set, stability radius of a problem, Hölder norm, Chebyshev norm.
DOI: 10.17377/daio.2015.22.467
Sergey E. Bukhtoyarov 1
Vladimir A. Emelichev 1
1. Belarusian State University,
4 Nezavisimosti Ave., 220030 Minsk, Belarus
å-mail: emelichev@tut.by
Received 15 November 2014
References
[1] V. A. Emelichev and V. V. Korotkov, Stability analysis of a Pareto-optimal portfolio of the multicriteria investment problem with Wald maximin criteria, Diskretn. Anal. Issled. Oper., 19, No. 6, 23–36, 2012.[2] V. A. Emelichev and V. V. Korotkov, Stability radius of a vector investment problem with Savage minimax risk criteria, Kibern. Sist. Anal., No. 3, 68–77, 2012. Translated in Cybern. Syst. Anal., 48, No. 3, 378–386, 2012.
[3] V. A. Emelichev and V. V. Korotkov, On stability of a vector Boolean investment problem with Wald criteria, Diskretn. Mat., 24, No. 3, 3–16, 2012. Translated in Discrete Math. Appl., 22, No. 4, 367–381, 2012.
[4] V. A. Emelichev and D. P. Podkopaev, Stability and regularization of vector integer programs, Diskretn. Anal. Issled. Oper., Ser. 2, 8, No. 1, 47–69, 2001.
[5] V. V. Podinovski and V. D. Nogin, Pareto-optimal’nye resheniya mnogokriterial’nykh zadach (Pareto-Optimal Solutions ofMulticriteria Problems), FIZMATLIT, Moscow, 2007.
[6] G. H. Hardy, J. E. Littlewood, and G. P´olya, Inequalities, Cambridge Univ. Press, Cambridge, 1934. Translated under the title Neravenstva, Izdatel’stvo Inostr. Lit., Moscow, 1948.
[7] V. A. Emelichev and V. V. Korotkov, On stability of multicriteria investment Boolean problem with Wald’s efficiency criteria, Bul. Acad. Ştiinţe Repub. Mold., Mat., No. 1, 3–13, 2014.
[8] V. A. Emelichev and V. V. Korotkov, On stability radius of the multicriteria variant of Markowitz’s investment portfolio problem, Bul. Acad. Ştiinţe Repub. Mold., Mat., No. 1, 83–94, 2011.
[9] V. A. Emelichev and D. P. Podkopaev, Quantitative stability analysis for vector problems of 0-1 programming, Discrete Optim., 7, No. 1–2, 48–63, 2010.
[10] H. M. Markowitz, Portfolio Selection: Efficient Diversification of Invest- ments, Blackwell Publ., Oxford, 1991.
