Optimal investment models with vintage capital: Dynamic programming approach
AbstractThe 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 ([Barucci and Gozzi, 1998], [Barucci and Gozzi, 2001], [Feichtinger et al., 2003] and [Feichtinger et al., 2006]) 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 by (Faggian, 2005b) and (Faggian, 2008a). 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. Finally it is explained how the results can be applied to improve the analysis of the optimal paths previously performed by Barucci and Gozzi and by Feichtinger et al.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 46 (2010)
Issue (Month): 4 (July)
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Web page: http://www.elsevier.com/locate/jmateco
Optimal investment Vintage capital Age-structured systems Optimal control Dynamic programming Hamilton-Jacobi-Bellman equations Linear convex control Boundary control;
Other versions of this item:
- Silvia Faggian & Fausto Gozzi, 2008. "Optimal investment models with vintage capital: Dynamic Programming approach," Working Papers 174, Department of Applied Mathematics, Università Ca' Foscari Venezia.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Capital; Investment; Capacity
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