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Tr. Mat. Inst. Steklova, 2014, Volume 284, Pages 56–88 (Mi tm3517)  

This article is cited in 7 scientific papers (total in 7 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

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.


DOI: https://doi.org/10.1134/S037196851401004X

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 284, 50–80

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received in June 2013

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, Tr. 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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\vol 284
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\publ MAIK Nauka/Interperiodica
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 22–39  mathnet  crossref  mathscinet  isi  elib
    2. 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
    3. 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
    4. 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
    5. 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
    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  isi  elib
    7. 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  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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