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Sibirskii Zhurnal Industrial'noi Matematiki, 2009, Volume 12, Number 3, Pages 75–84 (Mi sjim569)  

The Distribution of an Indivisible Resource: Optimal Control and Prices

È. O. Rapoport

Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
References:
Abstract: We study a dynamical system of economics with discrete time, whose states at every moment are characterized by integer nonnegative points in a two-dimensional vector space. There are two types of goods and two different production facilities, in each of which the state of the system can change by some random integer vector with various collections of probabilities. By a control we understand choosing at every moment one of the available collections of probabilities. The aim of control is to minimize the probability of leaving the positive quadrant. We study the existence of prices for the goods which agree with the optimal control.
Keywords: optimal control, prices, Markov chain.
Received: 28.11.2008
English version:
Journal of Applied and Industrial Mathematics, 2010, Volume 4, Issue 3, Pages 380–388
DOI: https://doi.org/10.1134/S1990478910030105
Bibliographic databases:
UDC: 519.866.6+519.873
Language: Russian
Citation: È. O. Rapoport, “The Distribution of an Indivisible Resource: Optimal Control and Prices”, Sib. Zh. Ind. Mat., 12:3 (2009), 75–84; J. Appl. Industr. Math., 4:3 (2010), 380–388
Citation in format AMSBIB
\Bibitem{Rap09}
\by \`E.~O.~Rapoport
\paper The Distribution of an~Indivisible Resource: Optimal Control and Prices
\jour Sib. Zh. Ind. Mat.
\yr 2009
\vol 12
\issue 3
\pages 75--84
\mathnet{http://mi.mathnet.ru/sjim569}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2668787}
\transl
\jour J. Appl. Industr. Math.
\yr 2010
\vol 4
\issue 3
\pages 380--388
\crossref{https://doi.org/10.1134/S1990478910030105}
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    Сибирский журнал индустриальной математики
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