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Solving internal habit formation models through dynamic programming in infinite dimension.

Augeraud-Veron, E. and Bambi, M. and Gozzi, F. (2017) 'Solving internal habit formation models through dynamic programming in infinite dimension.', Journal of optimization theory and applications., 173 (2). pp. 584-611.


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.

Item Type:Article
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Publisher statement:This is a post-peer-review, pre-copyedit version of an article published in Journal of Optimization Theory and Applications. The final authenticated version is available online at:
Date accepted:27 January 2017
Date deposited:21 August 2018
Date of first online publication:10 February 2017
Date first made open access:21 August 2018

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