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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

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

This article is cited 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

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.

UDC: 517.977

Received in June 2013

DOI: 10.1134/S037196851401004X


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

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