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

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

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UDC: 517.977

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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• http://mi.mathnet.ru/eng/tm3517
• https://doi.org/10.1134/S037196851401004X
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This publication is cited in the following articles:
1. Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 22–39
2. S. M. Aseev, “Adjoint variables and intertemporal prices in infinite-horizon optimal control problems”, Proc. Steklov Inst. Math., 290:1 (2015), 223–237
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
4. S. M. Aseev, “On the boundedness of optimal controls in infinite-horizon problems”, Proc. Steklov Inst. Math., 291 (2015), 38–48
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
6. K. O. Besov, “On Balder's Existence Theorem for Infinite-Horizon Optimal Control Problems”, Math. Notes, 103:2 (2018), 167–174
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
8. 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
9. 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
10. S. M. Aseev, “Printsip maksimuma dlya zadachi optimalnogo upravleniya s asimptoticheskim kontsevym ogranicheniem”, Tr. IMM UrO RAN, 27, no. 2, 2021, 35–48
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