Econometrica: Sep, 1987, Volume 55, Issue 5

Existence Results and Finite Horizon Approximates for Infinite Horizon Optimization Problems

https://doi.org/0012-9682(198709)55:5<1187:ERAFHA>2.0.CO;2-W
p. 1187-1209

Roger J-B. J-B. Wets, Sjur D. Flam

The paper deals with infinite horizon optimization problems. The existence of optimal solutions is obtained as a consequence of an asymptotic growth condition. We also construct finite horizon approximates that yield upper and lower bounds for the optimal values and whose optimal solutions converge to the long-term optimal trajectories. One type of approximate results from a process which involves smoothening the tail of any trajectory. The other type emerges when we restrain ourselves to stay put after a finite lapse of time.