phone +7 (3412) 91 60 92

Archive of Issues


Russia Moscow; Orekhovo-Zuevo
Year
2017
Volume
27
Issue
1
Pages
3-16
>>
Section Mathematics
Title A new approach to multicriteria problems under uncertainty
Author(-s) Vysokos M.I.a, Zhukovskii V.I.b, Kirichenko M.M.b, Samsonov S.P.b
Affiliations Moscow State Regional Institute of Humanitiesa, Lomonosov Moscow State Universityb
Abstract The applicability and novelty of this research lies in that the decision-maker in a multicriteria problem aims not only to maximize guaranteed values of each criterion, but also to minimize the guaranteed risks accompanying the said maximization. The topic of the research lies at the interface of the multicriteria problem theory and the Savage-Niehans minimax regret principle: the concept of a weakly effective estimate has been derived from the MP theory, while estimation of risks with values of the Savage-Niehans regret function has been derived from the minimax regret principle. The scope of this research is limited to interval uncertainties: the decision-maker only knows the limits of the interval, and probabilistic characteristics are missing. A new term is introduced, namely, “strongly guaranteed solution under outcomes and risks”; its existence for “regular”-confined-strategies for the mathematical programming is established. As an example of a practical application, the problem of diversification of a multi-currency deposit is suggested and solved.
Keywords multicriteria problems, strong guarantee, Slater and Pareto maximum, minimax regret, deposit diversification
UDC 519.858
MSC 90C29
DOI 10.20537/vm170101
Received 11 December 2016
Language Russian
Citation Vysokos M.I., Zhukovskii V.I., Kirichenko M.M., Samsonov S.P. A new approach to multicriteria problems under uncertainty, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 1, pp. 3-16.
References
  1. Wald A. Contribution to the theory of statistical estimation testing hypothesis, The Annals of Mathematical Statistics, 1939, vol. 10, pp. 299-326. DOI: 10.1214/aoms/1177732144
  2. Niehans J. Zur preisbildung bei ungewissen erwartungen, Schweizerische Zeitschrift für Volkswirtschaft und Statistik, 1948, vol. 84, no. 5. pp. 433-456.
  3. Savage L.J. The theory of statistical decision, Journal of the American Statistical Association, 1951, vol. 46, issue 253, pp. 55-67. DOI: 10.2307/2280094
  4. Cheremnykh Yu.N. Mikroekonomika. Prodvinutyi uroven' (Microeconomics. Advanced level), Moscow: Infra, 2008, 843 p.
  5. Zhukovskii V.I. Riski v konfliktnykh situatsiyakh (Risks in conflict situations), Moscow: URSS, 2011, 330 p.
  6. Sirazetdinov T.K., Sirazetdinov R.T. Problems of risk and its modeling, Problemy Chelovecheskogo Riska, 2007, no. 1, pp. 31-43 (in Russian).
  7. Shakhov V.V. Vvedenie v strakhovanie. Ekonomicheskii aspekt (Introduction to insurance. Economic aspect), Moscow: Finansy i Statistika, 2001, 286 p.
  8. Tsvetkova E.V., Arlyukova N.O. Risk v ekonomicheskoi deyatel'nosti (The risk in economic activity), St. Petersburg: Institute of Foreign Economic Relations, Economics and Law, 2002, 64 p.
  9. Markowitz H. Portfolio selection, The Journal of Finance, 1952, vol. 7, no. 1, pp. 77-91. DOI: 10.2307/2975974
  10. Zhukovskiy V.I., Kudryavtsev K.N. Equilibrating conflicts under uncertainty. I. Analogue of a saddle-point, Mat. Teor. Igr Pril., 2013, vol. 5, issue 1, pp. 27-44 (in Russian).
  11. Zhukovskiy V.I., Kudryavtsev K.N. Equilibrating conflicts under uncertainty. II. Analogue of a maximin, Mat. Teor. Igr Pril., 2013, vol. 5, issue 2, pp. 3-45 (in Russian).
  12. Zhukovskii V.I., Salukvadze M.E. The vector-valued maximin, New York etc.: Academic Press, 1994, 404 p. DOI: 10.1016/s0076-5392(08)x6114-4
  13. Morozov V.V., Sukharev A.G., Fedorov V.V. Issledovanie operatsii v zadachakh i uprazhneniyakh (Operations research in tasks and exercises), Moscow: Vysshaya Shkola, 1986, 285 p.
  14. Podinovskii V.V., Nogin V.D. Pareto-optimal'nye resheniya mnogokriterial'nykh zadach (Pareto optimal solutions of multicriteria problems), Moscow: Fizmatgiz, 2007, 255 p.
  15. Arrow K.J., Hurwicz L., Uzawa H. Studies in linear and nonlinear programming, Stanford: Stanford University Press, 1958. Translated under the title Issledovaniya po lineinomu i nelineinomu programmirovaniyu, Moscow: Inostr. Lit., 1962, 336 p.
  16. Zhukovskii V.I., Molostvov V.S., Topchishvili A.L. Problem of multicurrency deposit diversification - three possible approaches to risk accounting, International Journal of Operations and Quantitative Management, 2014, vol. 20, no. 1, pp. 1-15.
  17. Kapitonenko V.V. Finansovaya matematika i ee prilozheniya (Financial mathematics and its applications), Moscow: Prior, 2000, 140 p.
  18. Zhukovskii V.I., Kirichenko M.M. Risks and outcomes in multicriteria problem under uncertainty, Upravlenie Riskom, 2016, vol. 18, no. 2, pp. 17-28 (in Russian).
Full text
Next article >>