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Tr. Mat. Inst. Steklova, 2015, Volume 291, Pages 56–68 (Mi tm3659)  

This article is cited in 1 scientific paper (total in 1 paper)

Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump

K. O. Besov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: In 2013, S. Aseev, K. Besov, and S. Kaniovski (“The problem of optimal endogenous growth with exhaustible resources revisited,” Dyn. Model.Econometr. Econ. Finance 14, 3–30) considered the problem of optimal dynamic allocation of economic resources in an endogenous growth model in which both production and research sectors require an exhaustible resource as an input. The problem is formulated as an infinite-horizon optimal control problem with an integral constraint imposed on the control. A full mathematical study of the problem was carried out, and it was shown that the optimal growth is not sustainable under the most natural assumptions about the parameters of the model. In the present paper we extend the model by introducing an additional possibility of “random” transition (jump) to a qualitatively new technological trajectory (to an essentially unlimited backstop resource). As an objective functional to be maximized, we consider the expected value of the sum of the objective functional in the original problem on the time interval before the jump and an evaluation of the state of the model at the moment of the jump. The resulting problem also reduces to an infinite-horizon optimal control problem, and we prove an existence theorem for it and write down an appropriate version of the Pontryagin maximum principle. Then we characterize the optimal transitional dynamics and compare the results with those for the original problem (without a jump).

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968515040056

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 291, 49–60

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: October 15, 2015

Citation: K. O. Besov, “Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump”, Optimal control, Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 291, MAIK Nauka/Interperiodica, Moscow, 2015, 56–68; Proc. Steklov Inst. Math., 291 (2015), 49–60

Citation in format AMSBIB
\Bibitem{Bes15}
\by K.~O.~Besov
\paper Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump
\inbook Optimal control
\bookinfo Collected papers. In commemoration of the 105th anniversary of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 291
\pages 56--68
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3659}
\crossref{https://doi.org/10.1134/S0371968515040056}
\elib{http://elibrary.ru/item.asp?id=24776662}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2015
\vol 291
\pages 49--60
\crossref{https://doi.org/10.1134/S0081543815080052}
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    This publication is cited in the following articles:
    1. 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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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