Optimal investment models with vintage capital: Dynamic Programming approach

Faggian, Silvia and Gozzi, Fausto (2008) Optimal investment models with vintage capital: Dynamic Programming approach. [Working Paper]. Universita degli Studi di Venezia (Ca' Foscari), Dipartimento di Matematica Applicata, Venezia. p. 34. Working Papers (n. 174/2008).

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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.

Item Type: Report / Paper (Working Paper)
Research documents and activity classification: Working Papers > Refereed Working Papers / of international relevance
Divisions: Department of Business and Management
Additional Information: The definitve version of this paper has been published in "Journal of Mathematical Economics", Volume 46, Issue 4, 20 July 2010, Pages 416-437
MIUR Scientific Area: Area 13 - Economics and Statistics > SECS-S/06 Mathematics for Economics, Actuarial Studies and Finance
Deposited by: Maria Teresa Nisticò
Date Deposited: 30 Nov 2010 13:59
Last Modified: 21 Apr 2015 23:13
URI: http://eprints.luiss.it/id/eprint/761


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