Geodesic
Markowitz investment Boolean problem in case of uncertainty, multicriteria and risk
Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 115-122.

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Lower and upper bounds are obtained for the stability radius of a Pareto optimal portfolio of multicriteria variant of Markowitz problem with Savage minimax risk criteria in the case of any Hölder metric $l_p$, $1\leq p\leq\infty$, in the portfolio space and Chebyshev metric in the risk and market state spaces.
Keywords: multicriteria investment problem, Pareto optimal portfolio, Savage risk criteria, stability radius of portfolio, Hölder metric. 
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V. A. Emelichev; R. P. Shatsov. Markowitz investment Boolean problem in case of uncertainty, multicriteria and risk. Prikladnaâ diskretnaâ matematika, no. 2 (2013), pp. 115-122. http://geodesic.mathdoc.fr/item/PDM_2013_2_a11/

[1] Emelichev V. A., Korotkov V. V., “Issledovanie ustoichivosti reshenii vektornoi investitsionnoi bulevoi zadachi v sluchae metriki Geldera v kriterialnom prostranstve”, Prikladnaya diskretnaya matematika, 2012, no. 4, 61–72

[2] Markowitz H., “Portfolio selection”, J. Finance, 7:1 (1952), 77–91

[3] Markowitz H. M., Portfolio selection: efficient diversification of investments, Willey, New York, 1991, 400 pp.

[4] Sharp U. F., Aleksander G. Dzh., Beili D. V., Investitsii, Infra-M, M., 2003, 1028 pp.

[5] A. Salo, J. Keisler, A. Morton (eds.), Portfolio decision analysis: improved methods for resource allocation, International Series in Operations Research and Management Science, Springer, New York, 2011, 424 pp. | DOI

[6] Tepman L. N., Riski v ekonomike, YuNITI-DANA, M., 2002, 380 pp.

[7] Shapkin A. S., Ekonomicheskie i finansovye riski, Dashkov i Ko, M., 2003, 544 pp.

[8] Bronshtein E. M., Kachkaeva M. M., Tulupova E. V., “Upravlenie portfelem tsennykh bumag na osnove kompleksnykh kvantilnykh mer riska”, Izvestiya RAN. Teoriya i sistemy upravleniya, 2011, no. 1, 178–183 | MR

[9] Derevyanko P. M., Otsenka proektov v usloviyakh neopredelennosti, Korporativnyi menedzhment [Elektronnyi resurs] , 2006, Data dostupa: 06.02.13 http://www.cfin.ru/finanalysis/invest/fuzzy_analysis.shtml/

[10] Savage L. J., The foundations of statistics, Dover Publ., New York, 1972, 310 pp. | MR | Zbl

[11] Demyanov V. F., Malozemov V. N., Vvedenie v minimaks, Nauka, M., 1972, 368 pp. | MR

[12] Fedorov V. V., Chislennye metody maksimina, Nauka, M., 1979, 280 pp. | MR

[13] D.-Z. Du, P. M. Pardalos (eds.), Minimax and applications, Kluwer Acad. Publ., Dordrecht, 1995, 308 pp. | MR

[14] Sukharev A. G., Minimaksnye algoritmy v zadachakh chislennogo analiza, Librokom, M., 2009, 304 pp.

[15] Emelichev V. A., Kuzmin K. G., “O radiuse ustoichivosti effektivnogo resheniya vektornoi zadachi tselochislennogo lineinogo programmirovaniya v metrike Gëldera”, Kibernetika i sistemnyi analiz, 2006, no. 4, 175–181 | Zbl

[16] Emelichev V. A., Korotkov V. V., Kuzmin K. G., “Mnogokriterialnaya investitsionnaya zadacha v usloviyakh neopredelennosti i riska”, Izvestiya RAN. Teoriya i sistemy upravleniya, 2011, no. 6, 157–164 | MR

[17] Emelichev V. A., Korotkov V. V., “O radiuse ustoichivosti effektivnogo resheniya mnogokriterialnoi zadachi portfelnoi optimizatsii s kriteriyami Sevidzha”, Diskretnaya matematika, 23:4 (2011), 33–38 | DOI | MR | Zbl

[18] Emelichev V. A., Korotkov V. V., “Postoptimalnyi analiz vektornoi investitsionnoi zadachi s maksiminnymi kriteriyami Valda”, Diskretnyi analiz i issledovanie operatsii, 19:6 (2012), 23–36

[19] Emelichev V. A., Kuzmin K. G., “Obschii podkhod k issledovaniyu ustoichivosti pareto-optimalnogo resheniya vektornoi zadachi tselochislennogo lineinogo programmirovaniya”, Diskretnaya matematika, 19:3 (2007), 79–83 | DOI | MR | Zbl

[20] Emelichev V., Korotkov V., Kuzmin K., “On stability of a Pareto-optimal solution of a portfolio optimization problem with Savage's minimax risk criteria”, Bulletin of the Academy of Sciences of Moldova. Mathematics, 2010, no. 3(64), 35–44 | MR | Zbl

[21] Emelichev V. A., Korotkov V. V., “Ob ustoichivosti effektivnogo resheniya vektornoi investitsionnoi bulevoi zadachi s minimaksnymi kriteriyami Sevidzha”, Trudy Instituta matematiki NAN Belarusi, 18:2 (2010), 3–10 | Zbl

[22] Larichev O. I., Teoriya i metody prinyatiya reshenii, Logos, M., 2002, 392 pp.

[23] Nogin V. D., Prinyatie reshenii v mnogokriterialnoi srede: kolichestvennyi podkhod, Fizmatlit, M., 2002, 144 pp.