 Solving Internal Habit Formation Models Through Dynamic Programming in Infinite DimensionEmmanuelle Augeraud-Véron, Mauro Bambi and Fausto Gozzi Post-Print from HAL Abstract: In this paper, we study an economic model, where internal habits play a role. Their formation is described by a more general functional form than is usually assumed in the literature, because a finite memory effect is allowed. Indeed, the problem becomes the optimal control of a standard ordinary differential equation, with the past of the control entering both the objective function and an inequality constraint. Therefore, the problem is intrinsically infinite dimensional. To solve this model, we apply the dynamic programming approach and we find an explicit solution for the associated Hamilton–Jacobi–Bellman equation, which lets us write the optimal strategies in feedback form. Therefore, we contribute to the existing literature in two ways. Firstly, we fully develop the dynamic programming approach to a type of problem not studied in previous contributions. Secondly, we use this result to unveil the global dynamics of an economy characterized by generic internal habits. Keywords: Optimal control problems with delay; Dynamic programming; Habit formation (search for similar items in EconPapers) Published in Journal of Optimization Theory and Applications, inPress, 173 (2), pp.584-611. ⟨10.1007/s10957-017-1073-8⟩ There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02871232 DOI: 10.1007/s10957-017-1073-8 Access Statistics for this paper More papers in Post-Print from HAL |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.