On stability of multicriteria investment Boolean problem with Wald's efficiency criteria
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2014), pp. 3-13.

Voir la notice de l'article provenant de la source Math-Net.Ru

Based on Markowitz's portfolio theory we construct the multicriteria Boolean problem with Wald's maximin efficiency criteria and the Pareto-optimality principle. We obtained lower and upper attainable bounds for the stability radius of the problem in the cases of linear metric $l_1$ in the portfolio and the market state spaces and of the Chebyshev metric $l_\infty$ in the criteria space.
@article{BASM_2014_1_a0,
     author = {Vladimir Emelichev and Vladimir Korotkov},
     title = {On stability of multicriteria investment {Boolean} problem with {Wald's} efficiency criteria},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {3--13},
     publisher = {mathdoc},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2014_1_a0/}
}
TY  - JOUR
AU  - Vladimir Emelichev
AU  - Vladimir Korotkov
TI  - On stability of multicriteria investment Boolean problem with Wald's efficiency criteria
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2014
SP  - 3
EP  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2014_1_a0/
LA  - en
ID  - BASM_2014_1_a0
ER  - 
%0 Journal Article
%A Vladimir Emelichev
%A Vladimir Korotkov
%T On stability of multicriteria investment Boolean problem with Wald's efficiency criteria
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2014
%P 3-13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2014_1_a0/
%G en
%F BASM_2014_1_a0
Vladimir Emelichev; Vladimir Korotkov. On stability of multicriteria investment Boolean problem with Wald's efficiency criteria. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2014), pp. 3-13. http://geodesic.mathdoc.fr/item/BASM_2014_1_a0/

[1] Tikhonov A. N., Arsenin V. Y., Solutions of Ill-posed Problems, Wiley, New York, 1977 | MR | Zbl

[2] Lavrentiev M. M., Romanov V. G., Shishatskii S. P., Ill-Posed Problems in Mathematical Physics and Analysis, Nauka, Moscow, 1980

[3] Ivanov V. K., Vasin V. V., Tanana V. P., Theory of Linear Ill-Posed Problems and its Applications, Walter de Gruyter, Berlin, 2002

[4] Dubov J. A., Travkin S. I., Yakimec V. N., Multicriteria Models of Making and Selection of System Alternative, Nauka, Moscow, 1986 | MR | Zbl

[5] Belousov E. G. Andronov V. G., Solvability and Stability for Problems of Polynomial Programming, Moscow University, Moscow, 1993 | MR | Zbl

[6] Tanino T., Sawaragi Y., “Stability of nondominated solutions in multicriteria decision making”, J. Optim. Theory Appl., 30:2 (1980), 229–253 | DOI | MR | Zbl

[7] Sergienko I. V., Kozeratskaya L. N., Lebedeva T. T., Stability and Parametric Analysis of Discrete Optimization Problems, Naukova Dumka, Kiev, 1995

[8] Sergienko I. V., Shilo V. P., Discrete Optimization Problems: Challenges, Solution Techniques, and Investigations, Naukova Dumka, Kiev, 2003

[9] Sotskov Yu. N., Sotskova N. Yu., Lai T.-C., Werner F., Scheduling Under Uncertainty. Theory and Algorithms, Belorusskaya nauka, Minsk, 2010

[10] Sotskov Yu. N., Leontev V. K., Gordeev E. N., “Some concepts of stability analysis in combinatorial optimization”, Discrete Appl. Math., 58:2 (1995), 169–190 | DOI | MR | Zbl

[11] Sotskov Yu. N., Tanaev V. S., Werner F., “Stability radius of an optimal schedule: a survey and recent developments”, Industrial Applications of Combinatorial Optimization, Kluwer, Dordrecht, 1998, 72–108 | DOI | MR | Zbl

[12] Emelichev V. A., Girlich E., Nikulin Yu. V., Podkopaev D. P., “Stability and regularization of vector problems of integer linear programming”, Optimization, 51:4 (2002), 645–676 | DOI | MR | Zbl

[13] Greenberg H. J., “A bibliography for the development of an intelligent mathematical programming system”, Annals of Operations Research, 65:1 (1996), 55–90 | DOI | Zbl

[14] Greenberg H. J., “An annotated bibliography for post-solution analysis in mixed integer and combinatorial optimization”, Advances in Computational and Stochastic Optimization, Logic Programming, and Heuristic Search. Interfaces in Computer Science and Operations Research, ed. Woodruff D. L., Kluwer, Boston, 1998, 97–147 | MR | Zbl

[15] Emelichev V. A., Podkopaev D. P., “Stability and regularization of vector problems of integer linear programming”, Diskretnyi Analiz i Issledovanie Operatsii. Ser. 2, 8:1 (2001), 47–69 | MR | Zbl

[16] Emelichev V. A., Karelkina O. V., “Finite cooperative games: parametrisation of the concept of equilibrium (from Pareto to Nash) and stability of the efficient situation in the Holder metric”, Discrete Math. Appl., 19:3 (2009), 229–236 | DOI | MR | Zbl

[17] Emelichev V. A., Kuzmin K. G., “Stability radius of a vector integer linear programming problem: case of a regular norm in the space of criteria”, Cybernetics and Systems Analysis, 46:1 (2010), 72–79 | DOI | MR | Zbl

[18] Emelichev V., Podkopaev D., “Quantitative stability analysis for vector problems of 0-1 programming”, Discrete Optimization, 7:1–2 (2005), 48–63 | MR

[19] Emelichev V. A., Korotkov V. V., “On the stability radius of an efficient solution of a multicriteria portfolio optimisation problem with the Savage criteria”, Discrete Math. Appl., 21:5–6 (2011), 509–515 | DOI | MR | Zbl

[20] Emelichev V. A., Korotkov V. V., “Stability radius of a vector investment problem with Savage's minimax risk criteria”, Cybernetics and Systems Analysis, 48:3 (2012), 378–386 | DOI | MR

[21] Emelichev V. A., Korotkov V. V., “On stability of vector Boolean portfolio optimization problem with Savage's ordered risk criteria”, Proceedings of the National Academy of Sciences of Belarus. Series of Physical-Mathematical Sciences, 2012, no. 2, 42–47 | MR

[22] Emelichev V. A., Korotkov V. V., Kuz'min K. G., “Multicriterial investment problem in conditions of uncertainty and risk”, J. of Computer and System Sciences International, 50:6 (2011), 1011–1018 | DOI | MR | Zbl

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

[24] Emelichev V., Korotkov V., “On stability radius of the multicriteria variant of Markowitz's investment portfolio problem”, Bull. Acad. Sciences of Moldova, Mathematics, 2011, no. 1(65), 83–94 | MR | Zbl

[25] Emelichev V., Korotkov V., “Post-optimal analysis of investment problem with Wald's ordered maximin criteria”, Bull. Acad. Sciences of Moldova, Mathematics, 2012, no. 1(68), 59–69 | MR | Zbl

[26] Emelichev V. A., Korotkov V. V., “Sensitivity analyzis of lexicographical investment Boolean problem with Wald's maximin criteria”, Ukrainian Theoretical and Practical Conference “Informatics and System Sciences” (Poltava, Ukraine, March 1–3, 2012), 76–79

[27] Markowitz H. M., Portfolio Selection: Efficient Diversification of Investments, Blackwell, Oxford, 1991

[28] Carev V. V., The Estimation of Economic Efficiency of the Investment, Piter, Saint Petersburg, 2004

[29] Vilensky P. L., Livshiz V. N., Smolyk S. A., Evaluation of Investment Project Effectiveness, Theory and Practice, Moscow, 2008

[30] Bronshtein E. M., Kachkaeva M. M., Tulupova E. V., “Control of investment portfolio based on complex quantile risk measures”, J. of Computer and System Sciences International, 50:1 (2011), 174–180 | DOI | MR | Zbl

[31] Salo A., Keisler J., Morton A. (eds.), Portfolio Decision Analysis: Improved Methods for Resource Allocation, International series in operations research and management science, Springer, New York, 2011 | DOI

[32] Wald A., Statistical Decision Functions, Wiley, New York, 1950 | MR | Zbl

[33] Emelichev V. A., Korotkov V. V., “On stability radius of lexicographical Boolean problem in case $l_1$ metric in solution space”, Bull. of the Belarusian State University. Ser. 1, 2012, no. 1, 117–119

[34] Slater M., “Lagrange multipliers revisited”, Cowles foundation for research in economics at Yale University, Cowles foundation discussion papers, 80, Cowles foundation discussion paper: Mathematics 403, 1950 (reissue), 1980, 1–13

[35] Kolmogorov A. N., Fomin S. V., Elements of the Theory of Functions and Functional Analysis, Dover, New York, 1999 | Zbl