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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 284, Pages 56–88
DOI: https://doi.org/10.1134/S037196851401004X
(Mi tm3517)
 

This article is cited in 12 scientific papers (total in 12 papers)

On necessary optimality conditions for infinite-horizon economic growth problems with locally unbounded instantaneous utility function

K. O. Besov

Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
References:
Abstract: We consider a class of infinite-horizon optimal control problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of that kind the initial state is fixed, no constraints are imposed on the behavior of the admissible trajectories at infinity, and the objective functional is given by a discounted improper integral. Earlier, for such problems, S. M. Aseev and A. V. Kryazhimskiy in 2004–2007 and jointly with the author in 2012 developed a method of finite-horizon approximations and obtained variants of the Pontryagin maximum principle that guarantee normality of the problem and contain an explicit formula for the adjoint variable. In the present paper those results are extended to a more general situation where the instantaneous utility function need not be locally bounded from below. As an important illustrative example, we carry out a rigorous mathematical investigation of the transitional dynamics in the neoclassical model of optimal economic growth.
Funding agency Grant number
Russian Foundation for Basic Research
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Ministry of Education and Science of the Russian Federation
This work was supported by the Russian Foundation for Basic Research, the Ministry of Education and Science of the Russian Federation, and the Russian Academy of Sciences.
Received in June 2013
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 284, Pages 50–80
DOI: https://doi.org/10.1134/S0081543814010040
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: K. O. Besov, “On necessary optimality conditions for infinite-horizon economic growth problems with locally unbounded instantaneous utility function”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 56–88; Proc. Steklov Inst. Math., 284 (2014), 50–80
Citation in format AMSBIB
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\paper On necessary optimality conditions for infinite-horizon economic growth problems with locally unbounded instantaneous utility function
\inbook Function spaces and related problems of analysis
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2014
\vol 284
\pages 56--88
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://doi.org/10.1134/S037196851401004X
  • https://www.mathnet.ru/eng/tm/v284/p56
  • This publication is cited in the following 12 articles:
    1. Orlov S. Rovenskaya E., “Optimal Transition to Greener Production in a Pro-Environmental Society”, J. Math. Econ., 98 (2022), 102554  crossref  mathscinet  isi
    2. S. M. Aseev, “Maximum Principle for an Optimal Control Problem with an Asymptotic Endpoint Constraint”, Proc. Steklov Inst. Math. (Suppl.), 315, suppl. 1 (2021), S42–S54  mathnet  crossref  crossref  isi  elib
    3. S. M. Aseev, K. O. Besov, S. Yu. Kaniovski, “Optimal Policies in the Dasgupta–Heal–Solow–Stiglitz Model under Nonconstant Returns to Scale”, Proc. Steklov Inst. Math., 304 (2019), 74–109  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. L. Bagno, A. M. Tarasev, “Chislennye metody postroeniya funktsii tseny v zadachakh optimalnogo upravleniya na beskonechnom gorizonte”, Izv. IMI UdGU, 53 (2019), 15–26  mathnet  crossref  elib
    5. S. M. Aseev, V. M. Veliov, “Another view of the maximum principle for infinite-horizon optimal control problems in economics”, Russian Math. Surveys, 74:6 (2019), 963–1011  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. K. O. Besov, “On Balder's Existence Theorem for Infinite-Horizon Optimal Control Problems”, Math. Notes, 103:2 (2018), 167–174  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Alexander M. Lukatskii, 2018 Eleventh International Conference “Management of large-scale system development” (MLSD, 2018, 1  crossref
    8. S. M. Aseev, “Existence of an optimal control in infinite-horizon problems with unbounded set of control constraints”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 1–10  mathnet  crossref  crossref  mathscinet  isi  elib
    9. S. M. Aseev, “Adjoint variables and intertemporal prices in infinite-horizon optimal control problems”, Proc. Steklov Inst. Math., 290:1 (2015), 223–237  mathnet  crossref  crossref  zmath  isi  elib  elib
    10. K. O. Besov, “Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump”, Proc. Steklov Inst. Math., 291 (2015), 49–60  mathnet  crossref  crossref  isi  elib
    11. S. M. Aseev, “On the boundedness of optimal controls in infinite-horizon problems”, Proc. Steklov Inst. Math., 291 (2015), 38–48  mathnet  crossref  crossref  isi  elib
    12. Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 22–39  mathnet  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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