Infinite-horizon optimal control problems in economics. (English. Russian original) Zbl 1248.49023

Aseev, S. M.; Besov, K. O.; Kryazhimskij, A. V.

Russ. Math. Surv. 67, No. 2, 195-253 (2012); translation from Usp. Mat. Nauk 67, No. 2, 3-64 (2012).

Summary: 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 kind, the initial state is fixed, no constraints are imposed on the behavior 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.

MSC:

49K15	Optimality conditions for problems involving ordinary differential equations
91B62	Economic growth models
49K45	Optimality conditions for problems involving randomness
93E20	Optimal stochastic control

Keywords:

dynamic optimization; Pontryagin’s maximum principle; infinite horizon; transversality conditions at infinity; optimal economic growth