×

zbMATH — the first resource for mathematics

Markowitz investment Boolean problem in case of uncertainty, multicriteria and risk. (Russian. English summary) Zbl 07310209
Summary: 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.
MSC:
91 Game theory, economics, finance, and other social and behavioral sciences
49 Calculus of variations and optimal control; optimization
PDF BibTeX XML Cite
Full Text: MNR
References:
[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. · Zbl 1222.90004
[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
[9] Derevyanko P. M., Otsenka proektov v usloviyakh neopredelennosti, Korporativnyi menedzhment [Elektronnyi resurs]
[10] Savage L. J., The foundations of statistics, Dover Publ., New York, 1972, 310 pp. · Zbl 0276.62006
[11] Demyanov V. F., Malozemov V. N., Vvedenie v minimaks, Nauka, M., 1972, 368 pp.
[12] Fedorov V. V., Chislennye metody maksimina, Nauka, M., 1979, 280 pp.
[13] D.-Z. Du, P. M. Pardalos (eds.), Minimax and applications, Kluwer Acad. Publ., Dordrecht, 1995, 308 pp.
[14] Sukharev A. G., Minimaksnye algoritmy v zadachakh chislennogo analiza, Librokom, M., 2009, 304 pp. · Zbl 0717.65037
[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 1119.90029
[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
[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 · Zbl 1262.91124
[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 · Zbl 1278.90268
[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 · Zbl 1242.90105
[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 1223.90057
[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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.