Investment Boolean problem with Savage risk criteria under uncertainty
Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 20-33.

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

The portfolio theory is used to formulate a multicriteria investment Boolean escaped gain minimization problem for searching all extreme portfolios. Stability aspects of this set against perturbed parameters of minimax Savage criteria are studied. We give lower and upper estimates for the stability radius for arbitrary Hölder norms on the three-dimensional space of initial data.
Keywords: multicriteriality, investment Boolean problem, risks, collectively extremal set, extreme portfolio, stability radius of the problem, Hölder norm.
@article{DM_2019_31_2_a2,
     author = {V. A. Emelichev and S. E. Bukhtoyarov},
     title = {Investment {Boolean} problem with {Savage} risk criteria under uncertainty},
     journal = {Diskretnaya Matematika},
     pages = {20--33},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2019_31_2_a2/}
}
TY  - JOUR
AU  - V. A. Emelichev
AU  - S. E. Bukhtoyarov
TI  - Investment Boolean problem with Savage risk criteria under uncertainty
JO  - Diskretnaya Matematika
PY  - 2019
SP  - 20
EP  - 33
VL  - 31
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2019_31_2_a2/
LA  - ru
ID  - DM_2019_31_2_a2
ER  - 
%0 Journal Article
%A V. A. Emelichev
%A S. E. Bukhtoyarov
%T Investment Boolean problem with Savage risk criteria under uncertainty
%J Diskretnaya Matematika
%D 2019
%P 20-33
%V 31
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2019_31_2_a2/
%G ru
%F DM_2019_31_2_a2
V. A. Emelichev; S. E. Bukhtoyarov. Investment Boolean problem with Savage risk criteria under uncertainty. Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 20-33. http://geodesic.mathdoc.fr/item/DM_2019_31_2_a2/

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

[2] Sergienko I.V., Shilo V.P., Zadachi diskretnoi optimizatsii. Problemy, metody resheniya, issledovaniya, Naukova dumka, Kiev, 2003

[3] Sergienko I.V., Kozeratskaya L.N., Lebedeva T.T., Issledovanie ustoichivosti i parametricheskii analiz diskretnykh optimizatsionnykh zadach, Naukova dumka, Kiev, 1995

[4] Leontev V.K., “Diskretnaya optimizatsiya”, Zh. vychisl. matem. i matem. fiz., 47:2 (2007), 338–352 | MR | Zbl

[5] Gordeev E. N., “Comparison of three approaches to studying stability of solutions to problems of discrete optimization and computational geometry”, J. Applied and Industrial Mathematics, 9:3 (2015), 358–366 | DOI | MR | Zbl

[6] Emelichev V.A., Kotov V.M., Kuzmin K.G., Lebedeva T.T., Semenova N.V., Sergienko T.I., “Ustoichivost i effektivnye algoritmy resheniya zadach diskretnoi optimizatsii s mnogimi kriteriyami i nepolnoi informatsiei”, Problemy upravleniya i informatiki, 2014, no. 1, 53–67 | MR

[7] Emelichev V.A., Kuzmin K.G., Leonovich A.M., “Ustoichivost v vektornykh kombinatornykh zadachakh optimizatsii”, Avtomatika i telemekhanika, 2004, no. 2, 79–92 | Zbl

[8] Emelichev V. A., Gurevskij E. E., “On the stability kernel of a multicriteria combinatorial minimax problem”, J. Applied and Industrial Mathematics, 15:5 (2008), 6–19 | MR | Zbl

[9] Emelichev V.A., Kuzmin K.G., “O radiuse ustoichivosti vektornoi zadachi tselochislennogo lineinogo programmirovaniya v sluchae regulyarnosti normy v kriterialnom prostranstve”, Kibernetika i sistemnyi analiz, 2010, no. 1, 82–89 | MR | Zbl

[10] Emelichev V., Gurevsky E., Kuzmin K., “On stability of some lexicographic integer optimization problem”, Control and Cybernetics, 39:3 (2010), 811–826 | MR | Zbl

[11] Emelichev V., Karelkina O., Kuzmin K., “Qualitative stability analysis of multicriteria combinatorial minimum problems”, Control and Cybernetics, 41:1 (2012), 57–79 | MR | Zbl

[12] Gurevsky E., Battia O., Dolgui A., “Balancing of simple assembly lines under variations of task processing times”, Ann.Oper. Res., 2012, no. 201, 265–286 | DOI | MR | Zbl

[13] Lebedeva T.T., Semenova N.V., Sergienko T.I., “Ustoichivost vektornykh zadach tselochislennoi optimizatsii: vzaimosvyaz s ustoichivostyu mnozhestva optimalnykh i neoptimalnykh reshenii”, Kibernetika i sistemnyi analiz, 2005, no. 4, 90–100 | Zbl

[14] Lebedeva T.T., Sergienko T.I., “Raznye tipy ustoichivosti vektornoi zadachi tselochislennoi optimizatsii: obschii podkhod”, Kibernetika i sistemnyi analiz, 2008, no. 3, 142–148 | Zbl

[15] Libura M., van der Poort E., Sierksma G., van der Veen J., “Stability aspects of the travelling salesman problem based on $k$-best solutions”, Discrete Applied Mathematics, 87:1–3 (1998), 159–185 | DOI | MR | Zbl

[16] Leontev V.K., “Ustoichivost v lineinykh diskretnykh zadachakh”, Problemy kibernetiki, 35 (1979), 169–184, Moskva | Zbl

[17] Emelichev V.A., Podkopaev D.P., “Ustoichivost i regulyarizatsiya vektornykh zadach tselochislennogo lineinogo programmirovaniya”, Diskretnyi analiz i issledovanie operatsii. Ser.2, 8:1 (2001), 47–69 | MR | Zbl

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

[19] Emelichev V. A., Kuzmin K. G., “On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm”, J. Comput. Syst. Sci. Int., 46:5 (2007), 714–720 | DOI | MR

[20] Emelichev V. A., Kuzmin K. G., “A general approach to studying the stability of a Pareto optimal solution of a vector integer linear programming problem”, Discrete Math. Appl., 17:4 (2007), 349–354 | DOI | DOI | MR | Zbl

[21] Emelichev V., Podkopaev D.P., “Quantitative stability analysis for vector problems of 0-1 programming”, Discrete Optimization, 7:1-2 (2010), 48–63 | DOI | MR | Zbl

[22] Emelichev V. A., Kuzmin K. G., “Estimating the stability radius of the vector MAX-CUT problem”, Discrete Math. Appl., 23:2 (2013), 145–152 | DOI | DOI | MR | Zbl

[23] Emelichev V.A., Kuzmin K.G., “O radiuse $T_1$-ustoichivosti mnogokriterialnoi lineinoi bulevoi zadachi s normami Geldera v prostranstvakh parametrov”, Tavricheskii vestnik matematiki i informatiki, 2016, no. 1, 49–64

[24] Chakravarti N., Wagelmans A., “Calculation of stability radius for combinatorial optimization problems”, Oper. Res. Lett., 23:1 (1998), 1–7 | DOI | MR | Zbl

[25] Van Hoesel S., Wagelmans A., “On the complexity of postoptimality analysis of 0-1 programs”, Discr. Appl. Math., 91:1–3 (1999), 251–263 | MR | Zbl

[26] Roland J., De Smet Y., Rui Figueira J., “On the calculation of stability radius for multi-objective combinatorial optimization problems by inverse optimization”, J. Oper. Res., 10:4 (2012), 379–389 | DOI | MR | Zbl

[27] Emelichev V. A., Korotkov V. V., Kuzmin K. G., “Multicriterial investment problem in conditions of uncertainty and risk”, J. Comput. Syst. Sci. Int., 50:6 (2011), 1011–1018 | DOI | MR | Zbl

[28] Emelichev V. A., Korotkov V. V., “On stability of a vector Boolean investment problem with Wald’s criteria”, Discrete Math. Appl., 22:4 (2012), 367–381 | DOI | DOI | MR | MR | Zbl

[29] Emelichev V. A., Korotkov V. V., “O radiuse ustoichivosti vektornoi investitsionnoi zadachi s kriteriyami minimaksnogo riska Sevidzha”, Kibernetika i sistemnyi analiz, 2012, no. 3, 68–77 | MR | Zbl

[30] Emelichev V., Korotkov V., Nikulin Yu., “Post-optimal analysis for Markowitz multicriterio portfolio optimization problem”, J. Multi-Criteria Decision Analysis, 21 (2014), 95–100 | DOI

[31] Emelichev V., Korotkov V., “On stability of multicriteria investment Boolean problem with Wald's efficiency criteria”, Bull. Acad. Sci. Moldova. Mathematics, 2014, no. 1(74), 3–13 | MR | Zbl

[32] Emelichev V.A., Ustilko E.V., “Postoptimalnyi analiz investitsionnoi zadachi s kriteriyami krainego optimizma”, Prikladnaya diskretnaya matematika, 2014, no. 3, 117–123

[33] Bukhtoyarov S.E., Emelichev V.A., “On the stability measure of solutions to a vector version of an investment problem”, Jour. Appl. Industr. Math., 9:3 (2015), 328–334 | DOI | MR | Zbl

[34] Emelichev V., Bukhtoyarov S., Mychkov V., “An investment problem under multicriteriality, uncertainty and risk”, Bull. Acad. Sci. Moldova. Mathematics, 2016, no. 3, 82–98 | MR | Zbl

[35] Sholomov L.A., Logicheskie metody issledovaniya diskretnykh modelei, Nauka, Moskva, 1989

[36] Yudin D.B., Vychislitelnye metody teorii prinyatiya reshenii, Nauka, Moskva, 1989

[37] Aizerman M.A., Alekserov F.T., Vybor variantov: osnovy teorii, Nauka, Moskva, 1990 | MR

[38] Lotov A.V., Pospelova I.I., Mnogokriterialnye zadachi prinyatiya reshenii, MAKS Press, Moskva, 2008

[39] Tepman L.N., Riski v ekonomike, YuNITI-DANA, Moskva, 2002

[40] Shapkin A.S., Ekonomicheskie i finansovye riski, Dashkov i Ko, Moskva, 2013

[41] Moskvin V.A., Riski investitsionnykh proektov, KURS: INFRA-M, Moskva, 2016

[42] Howell L. (ed.), Global risks 2013, World Economic Forum, Geneva, 2012

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

[44] Du D., Pardalos P. (eds.), Minimax and applications, Kluwer, Dordrecht, 1995 | MR | Zbl

[45] Demyanov V. F., Malozemov V. N., Vvedenie v minimaks, Nauka, Moskva, 1972 | MR

[46] Pareto V., Manuel d'economie politique, V. Giard E. Briere, Paris, 1909

[47] Slater M., Lagrange multipliers revisited: a contribution to nonlinear programming. Cowles Comission Discussion Paper No. 80: Mathematics 403, Cowles Foundation for Research in Economics, Yale University, 1950

[48] Podinovskii V.V., Nogin V.D., Pareto-optimalnye resheniya mnogokriterialnykh zadach, FIZMATLIT, Moskva, 2007

[49] Bukhtoyarov S. E., Emelichev V. A., “Mera ustoichivosti lineinoi traektornoi zadachi s sovokupno-ekstremalnym printsipom optimalnosti”, Vestn. Belorus. gos. un-ta. Ser. 1, 2002, no. 3, 84–87 | MR

[50] 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

[51] Emelichev V.A., Mychkov V.I., “Postoptimalnyi analiz vektornogo varianta odnoi investitsionnoi zadachi”, Trudy In-ta matem. NAN Belarusi, 2016, no. 1, 9–18 | MR | Zbl