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Russian Mathematical Surveys, 2012, Volume 67, Issue 2, Pages 195–253
DOI: https://doi.org/10.1070/RM2012v067n02ABEH004785
(Mi rm9467)
 

This article is cited in 55 scientific papers (total in 56 papers)

Infinite-horizon optimal control problems in economics

S. M. Aseevab, K. O. Besova, A. V. Kryazhimskiyba

a Steklov Mathematical Institute of the Russian Academy of Sciences
b International Institute for Applied Systems Analysis, Laxenburg, Austria
References:
Abstract: This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the ‘standard’ limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices.
Bibliography: 53 titles.
Keywords: dynamic optimization, Pontryagin maximum principle, infinite horizon, transversality conditions at infinity, optimal economic growth.
Funding agency Grant number
Russian Foundation for Basic Research 09-01-00624-а
10-01-91004-АНФ-а
11-01-00348-а
11-01-12018-офи-м
Ministry of Education and Science of the Russian Federation НШ-65772.2010.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: 18.11.2011
Russian version:
Uspekhi Matematicheskikh Nauk, 2012, Volume 67, Issue 2(404), Pages 3–64
DOI: https://doi.org/10.4213/rm9467
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 49K15, 91B62
Language: English
Original paper language: Russian
Citation: S. M. Aseev, K. O. Besov, A. V. Kryazhimskiy, “Infinite-horizon optimal control problems in economics”, Uspekhi Mat. Nauk, 67:2(404) (2012), 3–64; Russian Math. Surveys, 67:2 (2012), 195–253
Citation in format AMSBIB
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\paper Infinite-horizon optimal control problems in economics
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\pages 3--64
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  • https://doi.org/10.1070/RM2012v067n02ABEH004785
  • https://www.mathnet.ru/eng/rm/v67/i2/p3
  • This publication is cited in the following 56 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
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    Abstract page:2052
    Russian version PDF:727
    English version PDF:73
    References:138
    First page:73
     
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