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 Tr. Mat. Inst. Steklova, 2008, Volume 262, Pages 16–31 (Mi tm762)

On a Class of Optimal Control Problems Arising in Mathematical Economics

S. M. Aseevab, A. V. Kryazhimskiiab

a Steklov Mathematical Institute, Russian Academy of Sciences
b International Institute for Applied Systems Analysis

Abstract: This paper is devoted to the study of the properties of the adjoint variable in the relations of the Pontryagin maximum principle for a class of optimal control problems that arise in mathematical economics. This class is characterized by an infinite time interval on which a control process is considered and by a special goal functional defined by an improper integral with a discounting factor. Under a dominating discount condition, we discuss a variant of the Pontryagin maximum principle that was obtained recently by the authors and contains a description of the adjoint variable by a formula analogous to the well-known Cauchy formula for the solutions of linear differential equations. In a number of important cases, this description of the adjoint variable leads to standard transversality conditions at infinity that are usually applied when solving optimal control problems in economics. As an illustration, we analyze a conventionalized model of optimal investment policy of an enterprise.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 262, 10–25

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Document Type: Article
UDC: 517.977

Citation: S. M. Aseev, A. V. Kryazhimskii, “On a Class of Optimal Control Problems Arising in Mathematical Economics”, Optimal control, Collected papers. Dedicated to professor Viktor Ivanovich Blagodatskikh on the occation of his 60th birthday, Tr. Mat. Inst. Steklova, 262, MAIK Nauka/Interperiodica, Moscow, 2008, 16–31; Proc. Steklov Inst. Math., 262 (2008), 10–25

Citation in format AMSBIB
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This publication is cited in the following articles:
1. S. M. Aseev, K. O. Besov, A. V. Kryazhimskiy, “Infinite-horizon optimal control problems in economics”, Russian Math. Surveys, 67:2 (2012), 195–253
2. Hespeler F., “On Boundary Conditions Within the Solution of Macroeconomic Dynamic Models with Rational Expectations”, Comput. Econ., 40:3 (2012), 265–291
3. Cruz-Rivera E. Vasilieva O., “Optimal Policies Aimed at Stabilization of Populations with Logistic Growth Under Human Intervention”, Theor. Popul. Biol., 83 (2013), 123–135
4. S. M. Aseev, “On some properties of the adjoint variable in the relations of the Pontryagin maximum principle for optimal economic growth problems”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 11–21
5. Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 22–39
6. Derev'yanko T.O., Kyrylych V.M., “Problem of Optimal Control For a Semilinear Hyperbolic System of Equations of the First Order With Infinite Horizon Planning”, Ukr. Math. J., 67:2 (2015), 211–229
7. Rokhlin D.B., Usov A., “Rational taxation in an open access fishery model”, Arch. Control Sci., 27:1 (2017), 5–27
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