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Maximum Principle for Boundary Control Problems Arising in Optimal Investment with Vintage Capital

Silvia Faggian

No 181, Working Papers from Department of Applied Mathematics, Università Ca' Foscari Venezia

Abstract: The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author et al. [26, 27, 28, 29, 30]. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is shown to coincide with the spatial gradient of the value function evaluated along the trajectory of the system, creating a parallel between Maximum Principle and Dynamic Programming. The abstract model applies, as recalled in one of the first sections, to optimal investment with vintage capital.

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: 18 pages
Date: 2008-11
New Economics Papers: this item is included in nep-dge, nep-mac and nep-ore
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Citations: View citations in EconPapers (7)

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