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On the bellman equation of the overtaking criterion

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Abstract

In this note, we discuss the properties of solutions to the Bellman's equation of the overtaking criterion and also prove that the optimal trajectory can be represented by a continuous dynamical system.

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References

  1. Ramsey, F.,A Mathematical Theory of Savings, Economic Journal, Vol. 38, pp. 543–559, 1928.

    Google Scholar 

  2. Montrucchio, L.,Optimal Decisions over Time and Strange Attractors: An Analysis by the Bellman Principle, Mathematical Modelling, Vol. 7, pp. 341–352, 1986.

    Google Scholar 

  3. Benhabib, J., andNishimura, K.,Competitive Equilibrium Cycles, Journal of Economic Theory, Vol. 35, pp. 284–306, 1985.

    Google Scholar 

  4. Boldrin, M., andMontrucchio, L.,On the Indeterminacy of Capital Accumulation Paths, Journal of Economic Theory, Vol. 40, pp. 26–39, 1986.

    Google Scholar 

  5. Deneckere, R., andPelikan, S.,Competitive Chaos, Journal of Economic Theory, Vol. 40, pp. 13–25, 1986.

    Google Scholar 

  6. Von Weizsacker, C. C.,Existence of Optimal Programs of Accumulation for an Infinite-Time Horizon, Review of Economic Studies, Vol. 32, pp. 85–104, 1965.

    Google Scholar 

  7. Gale, D.,On Optimal Development in a Multi-Sector Economy, Review of Economic Studies, Vol. 34, pp. 1–18, 1967.

    Google Scholar 

  8. Brock, W. A.,On Existence of Weakly Maximal Programs in a Multi-Sector Economy, Review of Economic Studies, Vol. 37, pp. 275–280, 1970.

    Google Scholar 

  9. McKenzie, L. W.,Optimal Economic Growth, Turnpike Theorems, and Comparative Dynamics, Handbook of Mathematical Economics, Edited by K. J. Arrow and M. D. Intriligator, North-Holland, Amsterdam, Holland, Vol. 3, pp. 1281–1358, 1986.

    Google Scholar 

  10. Berge, C.,Espaces Topologiques et Fonctions Multivoques, Dunod, Paris, France, 1959.

    Google Scholar 

  11. Rockafellar, R. T.,Convex Analysis, Princeton University Press, Princeton, New Jersey, 1972.

    Google Scholar 

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Communicated by W. Stadler

The authors thank P. Michel for helpful suggestions.

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Dana, R.A., Le Van, C. On the bellman equation of the overtaking criterion. J Optim Theory Appl 67, 587–600 (1990). https://doi.org/10.1007/BF00939651

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  • DOI: https://doi.org/10.1007/BF00939651

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