Equilibrium Points for Optimal Investment with Vintage Capital

Silvia Faggian

No 182, Working Papers from Department of Applied Mathematics, Università Ca' Foscari Venezia

Abstract: The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient conditions for existence of equilibrium points in the general case are given and later applied to the economic problem of optimal investment with vintage capital. Explicit computation of equilibria for the economic problem in some relevant examples is also provided. Indeed the challenging issue here is showing that a theoretical machinery, such as optimal control in infinite dimension, may be effectively used to compute solutions explicitly and easily, and that the same computation may be straightforwardly repeated in examples yielding the same abstract structure. No stability result is instead provided: the work here contained has to be considered as a first step in the direction of studying the behavior of optimal controls and trajectories in the long run.

Keywords: Linear convex control; Boundary control; Hamilton–Jacobi–Bellman equations; Optimal investment problems; Vintage capital (search for similar items in EconPapers)
JEL-codes: C61 C62 E22 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2008-11
New Economics Papers: this item is included in nep-bec and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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