Abstract
In this paper, we prove the necessity of a terminal condition for a solution of the Bellman Equation to be the value function in dynamic optimization problems with unbounded payoffs. We also state the weakest sufficient condition, which can be applied in a large class of problems, including economic growth, resource extraction, or human behaviour during an epidemic. We illustrate the results by examples, including simple linear–quadratic problems and problems of resource extraction, with multiple solutions to the Bellman Equation or the maximizer of the right hand side of the Bellman Equation with the actual value function being the worst control instead of being optimal.
Original language | English |
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Article number | 109332 |
Journal | Automatica |
Volume | 123 |
Number of pages | 10 |
ISSN | 0005-1098 |
DOIs | |
Publication status | Published - Jan 2021 |
Bibliographical note
Published online: 13 November 2020.Keywords
- Dynamic optimization
- Infinite horizon
- Unbounded payoffs
- Feedback controls
- Bellman Equation
- Terminal condition
- Necessity
- Sufficiency
- Resource extraction
- Fish Wars