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Dynamic Programming in Ordered Vector Space
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AI
DOI：10.1287/opre.2025.1971.png)
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Abstract
En 中文
New approaches to the theory of dynamic programming view dynamic programs as families of policy operators acting on partially ordered sets. In this paper, we extend these ideas by shifting from arbitrary partially ordered sets to ordered vector spaces. The integrated algebraic and order structure in such spaces leads to sharper fixed-point results. These fixed-point results can then be exploited to obtain optimality properties. We illustrate our results through applications ranging from firm management to data valuation. These applications include features from the recent literature on dynamic programming, including risksensitive preferences, nonlinear discounting, and state-dependent discounting. In all cases, we establish existence of optimal policies, characterize them in terms of Bellman optimality relationships, and prove convergence of major algorithms.
Keywords:
ordered vector space
Bellman equation
dynamic programming
Journal
O
IF:
2.6
Papers:
92
Citations:
1.5W