Infinite-horizon optimal control problems in economics

Aseev SM, Besov KO, & Kryazhimskiy AV (2012). Infinite-horizon optimal control problems in economics. Russian Mathematical Surveys 67 (2): 195-253. DOI:10.1070/RM2012v067n02ABEH004785.

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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.

Item Type: Article
Uncontrolled Keywords: Dynamic optimization; Pontryagin maximum principle; Infinite horizon; Transversality conditions at infinity; Optimal economic growth
Research Programs: Advanced Systems Analysis (ASA)
Bibliographic Reference: Russian Mathematical Surveys; 67(2):195-253
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 08:46
Last Modified: 25 Feb 2016 08:40
URI: http://pure.iiasa.ac.at/9921

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