Optimal strategies in linear multisector models: Value function and optimality conditions |
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Authors: | Giuseppe Freni Fausto Gozzi Cristina Pignotti |
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Institution: | 1. Dipartimento di Studi Economici, Facoltà di Economia, Università di Napoli “Parthenope”, via Medina 40, 80133 Napoli, Italy;2. Dipartimento di Scienze Economiche ed Aziendali, Facoltà di Economia, Università LUISS - Guido Carli, via Pola 12, 00198 Roma, Italy;3. Dipartimento di Matematica Pura e Applicata, Facoltà di Scienze MM.FF.NN., Università di L’Aquila, via Vetoio, Loc. Coppito, 67010 L’Aquila, Italy |
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Abstract: | In this paper we study an optimal control problem with mixed constraints related to a multisector linear model with endogenous growth. The main aim is to establish a set of necessary and a set of sufficient conditions which are the basis for studying the qualitative properties of optimal trajectories. The presence of possibly degenerate mixed constraints, the unboundedness and non-strict convexity of the Hamiltonian, make the problem difficult to deal with. We develop first the dynamic programming approach, proving that the value function is a bilateral viscosity solution to the associated Hamilton–Jacobi–Bellman (HJB) equation. Then, using our results, we give a set of sufficient and a set of necessary optimality conditions which involve so-called co-state inclusion: this can be interpreted as the existence of a dual path of prices supporting the optimal path. |
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Keywords: | C61 O41 |
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