Fundamentals of the linearization method for quantile analysis with small random parameters

Consideration was given to determination of the quantiles of the distribution of a nonlinear loss function of small random parameters. It was suggested to construct the quantile estimates using a linearized model where the problem under study comes to that of generalized linear programming. Precisio...

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Published in:	Automation and remote control Vol. 69; no. 8; pp. 1333 - 1343
Main Authors:	Kan, Yu. S., Sysuev, A. V.
Format:	Journal Article
Language:	English
Published:	Dordrecht SP MAIK Nauka/Interperiodica 01-08-2008
Subjects:	CAE) and Design Calculus of Variations and Optimal Control; Optimization Computer-Aided Engineering (CAD Control Mathematics Mathematics and Statistics Mechanical Engineering Mechatronics Robotics Stochastic Systems Systems Theory 02.50.Le
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Abstract	Consideration was given to determination of the quantiles of the distribution of a nonlinear loss function of small random parameters. It was suggested to construct the quantile estimates using a linearized model where the problem under study comes to that of generalized linear programming. Precision of these estimates was examined.
AbstractList	Consideration was given to determination of the quantiles of the distribution of a nonlinear loss function of small random parameters. It was suggested to construct the quantile estimates using a linearized model where the problem under study comes to that of generalized linear programming. Precision of these estimates was examined.
Author	Kan, Yu. S. Sysuev, A. V.
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References	KanYu.S.MartiK.Application of the Quantile Optimization to Bond Portfolio Selection Stochastic Optimization Techniques2002BerlinSpringer285308 Kan, Yu.S. and Sysuev, A.V., Comparison of the Quantile and Guaranteeing Approaches to System, Avtom. Telemekh., 2007, no. 1, pp. 126–143. KeinV.M.Optimizatsiya sistem upravleniya po minimaksnomu kriteriyu1985MoscowNauka(Optimization of the Control Systems by the Minimax Criterion) ZorichV.A.Matematicheskii analiz. I, II1984MoscowNauka(Mathematical Analysis. I, II) Kan, Yu.S. and Tuzov, N.V., Minimization of the Quantile of the Normal Distribution of the Bilinear Loss Function, Avtom. Telemekh., 1998, no. 11, pp. 82–92. Pankov, A.R., Platonov, E.R., and Semenikhin, K.V., Minimax Optimization of the Investment Portfolio by the Quantile Criterion, Avtom. Telemekh., 2003, no. 7, pp. 117–133. Vishnyakov, B.V. and Kibzun, A.I., Deterministic Equivalents for the Problems of Stochastic Programming with Probabilistic Criteria, Avtom. Telemekh., 2006, no. 6, pp. 126–143. MalyshevV.V.KibzunA.I.Analiz i sintez vysokotochnogo upravleniya letatel’nymi apparatami1987MoscowMashinostroenie(Precise Control of Flight Vehicles: Analysis and Design) Kan, Yu.S. and Krasnopol’skaya, A.N., On Generation of the Portfolio of Fixed-income Securities, Avtom. Telemekh., 2006, no. 4, pp. 97–104. EltonE.G.GruberM.J.Modern Portfolio Theory and Investment Analisis1991New YorkWiley KibzunA.I.KanYu.S.Stochastic Programming Problems with Probability and Quantile Functions1996New YorkWiley0885.90088 V.A. Zorich (8006_CR10) 1984 V.M. Kein (8006_CR4) 1985 8006_CR9 V.V. Malyshev (8006_CR1) 1987 A.I. Kibzun (8006_CR2) 1996 Yu.S. Kan (8006_CR8) 2002 8006_CR3 8006_CR11 8006_CR6 8006_CR7 E.G. Elton (8006_CR5) 1991
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SubjectTerms	CAE) and Design Calculus of Variations and Optimal Control; Optimization Computer-Aided Engineering (CAD Control Mathematics Mathematics and Statistics Mechanical Engineering Mechatronics Robotics Stochastic Systems Systems Theory
Title	Fundamentals of the linearization method for quantile analysis with small random parameters
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