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This article is cited in 55 scientific papers (total in 56 papers)
Infinite-horizon optimal control problems in economics
S. M. Aseevab, K. O. Besova, A. V. Kryazhimskiyba a Steklov Mathematical Institute of the Russian Academy of Sciences
b International Institute for Applied Systems Analysis, Laxenburg, Austria
Abstract:
This paper extends optimal control theory to a class of infinite-horizon problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of this sort the initial state is fixed, no constraints are imposed on the behaviour of the admissible trajectories at large times, and the objective functional is given by a discounted improper integral. We develop the method of finite-horizon approximations in a broad context and use it to derive complete versions of the Pontryagin maximum principle for such problems. We provide sufficient conditions for the normality of infinite-horizon optimal control problems and for the validity of the ‘standard’ limit transversality conditions with time going to infinity. As a meaningful example, we consider a new two-sector model of optimal economic growth subject to a random jump in prices.
Bibliography: 53 titles.
Keywords:
dynamic optimization, Pontryagin maximum principle, infinite horizon, transversality conditions at infinity, optimal economic growth.
Received: 18.11.2011
Citation:
S. M. Aseev, K. O. Besov, A. V. Kryazhimskiy, “Infinite-horizon optimal control problems in economics”, Uspekhi Mat. Nauk, 67:2(404) (2012), 3–64; Russian Math. Surveys, 67:2 (2012), 195–253
Linking options:
https://www.mathnet.ru/eng/rm9467https://doi.org/10.1070/RM2012v067n02ABEH004785 https://www.mathnet.ru/eng/rm/v67/i2/p3
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Abstract page: | 2051 | Russian version PDF: | 727 | English version PDF: | 72 | References: | 138 | First page: | 73 |
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