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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Maria Luisa Gota & Luigi Montrucchio, 1999. "On Lipschitz continuity of policy functions in continuous-time optimal growth models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 479-488.
  • 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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    Citations

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    Cited by:

    1. 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.
    2. Alain Venditti, 2012. "Weak concavity properties of indirect utility functions in multisector optimal growth models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 13-26, March.
    3. 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.
    4. 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.

    More about this item

    Keywords

    Optimal growth Policy functions.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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