Optimal investment models with vintage capital: Dynamic Programming approach

Silvia Faggian and Fausto Gozzi

No 174, Working Papers from Department of Applied Mathematics, Università Ca' Foscari Venezia

Abstract: The Dynamic Programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various papers (see e.g. [11, 12], [30, 32]) either in cases when explicit solutions can be found or using Maximum Principle techniques. The problem is rephrased into an infinite dimensional setting, it is proven that the value function is the unique regular solution of the associated stationary Hamilton-Jacobi-Bellman equation, and existence and uniqueness of optimal feedback controls is derived. It is then shown that the optimal path is the solution to the closed loop equation. Similar results were proven in the case of finite horizon in [26][27]. The case of infinite horizon is more challenging as a mathematical problem, and indeed more interesting from the point of view of optimal investment models with vintage capital, where what mainly matters is the behavior of optimal trajectories and controls in the long run. The study of infinite horizon is performed through a nontrivial limiting procedure from the corresponding finite horizon problems

Keywords: Optimal investment; vintage capital; age-structured systems; optimal control; dynamic programming; Hamilton-Jacobi-Bellman equations; linear convex control; boundary control (search for similar items in EconPapers)
JEL-codes: C61 C62 E22 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2008-11
New Economics Papers: this item is included in nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (79)

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Journal Article: Optimal investment models with vintage capital: Dynamic programming approach (2010)
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