Skip to Main Content

Modelling and Data Analysis
2020. Vol. 10, no. 3, 69–84
doi:10.17759/mda.2020100306
ISSN: 2219-3758 / 2311-9454 (online)

Statistical Simulation of the Probability Distribution Kernel and Its Application to Solve the Quantile Optimization Problem with the Bilinear Loss Function

84

P.A. Ardabyevskiy, D.A. Gonchar, Y.S. Kan

PDF (RUS)
Online translation in english
GS
Information
in Google Scholar

Abstract

The article considers a plane quantile optimization problem with a bilinear loss function, which, using suffi cient optimality conditions, is reduced to a linear programming problem. The reduction is based on the use of a polyhedral model of the kernel of the probability distribution of the vector of random parameters. To build this model, an algorithm based on the method of statistical modeling is proposed. A description of the software package for constructing a kernel model for a number of probability distributions of random parameters is given.

General Information

Keywords: quantile optimization, loss function, stochastic programming, kernel of probability distribution, minimax problem

Journal rubric: Optimization Methods

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2020100306

For citation: Ardabyevskiy P.A., Gonchar D.A., Kan Y.S. Statistical Simulation of the Probability Distribution Kernel and Its Application to Solve the Quantile Optimization Problem with the Bilinear Loss Function. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2020. Vol. 10, no. 3, pp. 69–84. DOI: 10.17759/mda.2020100306. (In Russ., аbstr. in Engl.)

References

  1. Kibzun A.I., Kan Y.S. Zadachi stohasticheskogo programmirovaniya s veroyatnostnymi kriteriyami. – M.: Fizmatlit, 2009.
  2. Kan Y.S. Formirovanie portfelej cennyh bumag s uchetom riska. M.: MAI publishing, 2008.
  3. Kan Y.S., Tuzov N.V. Minimizaciya kvantili normal’nogo raspredeleniya bilinejnoj funkcii poter’. Avtomatika i Telemekhanika. 1998, № 11, pp. 82–92.
  4. Vasil’eva S.N., Kan Y.S. Metod resheniya zadachi kvantil’noj optimizacii s bilinejnoj funkciej poter’ . Avtomatika i Telemekhanika, 2015, № 9, pp/ 83–101.
  5. Kan Y.S. Rasshirenie zadachi kvantil’noj optimizacii s linejnoj po sluchajnym parametram funkciej poter’ . Avtomatika i Telemekhanika, 2020, № 12.
  6. Vasil’eva S.N., Kan Y.S. Algoritm vizualizacii ploskogo yadra veroyatnostnoj mery. Informatika i ee primeneniya, 2018, № 2, pp. 60–68.

Information About the Authors

Pavel A. Ardabyevskiy, Student of the magistracy, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0000-0002-6857-7485, e-mail: ardpavel@gmail.com

Dmitry A. Gonchar, Student of the Magistracy, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0000-0002-2414-491X, e-mail: dima.gonchar.29.08.13@gmail.com

Yuri S. Kan, Doctor of Physics and Matematics, Professor, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID: https://orcid.org/0000-0001-9950-4716, e-mail: yu_kan@mail.ru

Metrics

Views

Total: 223
Previous month: 7
Current month: 5

Downloads

Total: 84
Previous month: 3
Current month: 0