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

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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

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