Existence and Uniqueness of Solutions to the Bellman Equation in the Unbounded Case.
We study the problem of the existence and uniqueness of solutions to the Bellman equation in the presence of unbounded returns. We introduce a new approach based both on consideration of a metric on the space of all continuous functions over the state space, and on the application of some metric fix...
| Published in: | Econometrica Vol. 71; no. 5; pp. 1519 - 1556 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Published: |
Wiley-Blackwell
September 2003
|
| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| Summary: | We study the problem of the existence and uniqueness of solutions to the Bellman equation in the presence of unbounded returns. We introduce a new approach based both on consideration of a metric on the space of all continuous functions over the state space, and on the application of some metric fixed point theorems. With appropriate conditions we prove uniqueness of solutions with respect to the whole space of continuous functions. Furthermore, the paper provides new sufficient conditions for the existence of solutions that can be applied to fairly general models. It is also proven that the fixed point coincides with the value function and that it can be approached by successive iterations of the Bellman operator. Reprinted by permission of the publisher. |
|---|