On Lipschitz continuity of policy functions in continuous-time optimal growth models

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On Lipschitz continuity of policy functions in continuous-time optimal growth models

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Maria Luisa Gota (Department of Applied Mathematics, University of Turin, Piazza Arbarello, 8, I-10122 Turin, ITALY)
Luigi Montrucchio (Department of Applied Mathematics, University of Turin, Piazza Arbarello, 8, I-10122 Turin, ITALY)

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Luigi Montrucchio

Abstract

This paper proves the C1,1 differentiability of the value function for continuous time concave dynamic optimization problems, under the assumption that the instantaneous utility is C1,1 and the initial segment of optimal solutions is interior. From this result, the Lipschitz dependence of optimal solutions on initial data and the Lipschitz continuity of the policy function are derived, by adding an assumption of strong concavity of the integrand.

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 14 (1999)
Issue (Month): 2 ()
Pages: 479-488
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Handle: RePEc:spr:joecth:v:14:y:1999:i:2:p:479-488

Note: Received: July 29, 1996; revised version: November 25, 1997
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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

Cited by:
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Colin Rowat, 2005. "Non-linear strategies in a linear quadratic differential game," GE, Growth, Math methods 0502001, EconWPA. [Downloadable!]
Other versions:
- Colin Rowat, 2005. "Non-Linear Strategies in a Linear Quadratic Differential Game," Discussion Papers 05-05, Department of Economics, University of Birmingham.
- Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3179-3202, October. [Downloadable!] (restricted)
Aliprantis, C.D. & Camera, G. & Ruscitti, F., 2007. "Monetary Equilibrium and the Differentiability of the Value Function," Purdue University Economics Working Papers 1199, Purdue University, Department of Economics. [Downloadable!]
Other versions:
- Aliprantis, C.D. & Camera, G. & Ruscitti, F., 2009. "Monetary equilibrium and the differentiability of the value function," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 454-462, February. [Downloadable!] (restricted)

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