Optimal Control in Infinite Dimensional Spaces and Economic Modeling: State of the Art and Perspectives

Giorgio Fabbri, Silvia Faggian (), Salvatore Federico and Fausto Gozzi
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Silvia Faggian: Ca’ Foscari University of Venice
Salvatore Federico: University of Bologna
Fausto Gozzi: Luiss University

No 2025: 16, Working Papers from Department of Economics, University of Venice "Ca' Foscari"

Abstract: This survey collects, within a unified framework, various results (primarily by the authors themselves) on the use of Deterministic Infinite-Dimensional Optimal Control Theory to address applied economic models. The main aim is to illustrate, through several examples, the typical features of such models (including state constraints, non-Lipschitz data, and non-regularizing differential operators) and the corresponding methods needed to handle them. This necessitates developing aspects of the existing Deterministic Infinite-Dimensional Optimal Control Theory (see, e.g., the book by Li and Yong, 2012) in specific and often nontrivial directions. Given the breadth of this area, we emphasize the Dynamic Programming Approach and its application to problems where explicit or quasi-explicit solutions of the associated Hamilton–Jacobi–Bellman (HJB) equations can be obtained. We also provide insights and references for cases where such explicit solutions are not available.

Keywords: Optimal Control in Infinite Dimensional Spaces; Dynamic Economic Modelling; Dynamic Programming; Hamilton-Jacobi-Bellman Equations (search for similar items in EconPapers)
JEL-codes: C61 E12 E22 (search for similar items in EconPapers)
Pages: 66 pages
Date: 2025
New Economics Papers: this item is included in nep-mac
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