Prof. Sergey Aseev, Steklov Mathematical Institute of RAS, Russia and International Institute for Applied System Analysis, Austria

Infinite-horizon optimal control problems arise naturally in studies of economic growth processes. Typically the Pontryagin maximum principle plays a role of the main tool. The aim of the course is to provide an introduction in the theory of the Pontryagin maximum principle with a focus on the methodology of its application in growth theory. The recently developed “finite-horizon approximation” approach to deriving a modified maximum principle targeted specifically to infinite-horizon problems of optimal control is presented. The attention is focused on the characterization of the behavior of Pontryagin’s adjoint variables (also treated as “shadow prices”) in a neighborhood of infinity. The developed methodology is illustrated by meaningful examples from growth theory.

Bibliography

1. S. M. Aseev, Infinite-horizon optimal control with applications in growth theory, MSU CMC Publications Department, Moscow, MAKS Press, 2009.
2. S.M. Aseev, A.V. Kryazhimskiy, The Pontryagin maximum principle and transversality conditions for a class of optimal control problems with infinite time horizons, SIAM Journal on Control and Optimization, 43, No. 3 (2004), 1094-1119.
3. S.M. Aseev, A.V. Kryazhimskiy, The Pontryagin maximum principle and optimal economic growth problems, Proceedings of the Steklov Institute of Mathematics, 257 (2007), 5-255.
4. D.A. Carlson, A.B. Haurie, A. Leizarowitz, Infinite Horizon Optimal Control. Deterministic and Stochastic Systems, Berlin, Springer, 1991.
5. H. Halkin, Necessary conditions for optimal control problems with infinite horizons, Econometrica, 42 (1974), 267—272.
6. L.S. Pontryagin, V.G. Boltyanskij, R.V. Gamkrelidze, E.F. Mishchenko, The mathematical theory of optimal processes, Oxford, Pergamon Press, 1964.
7. F.P. Ramsey, A mathematical theory of saving, Econ. J., 38 (1928) , 543—559.
8. A. Seierstad, K. Sydsæter, Optimal control theory with economic applications, Amsterdam, North-Holland, 1987.