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Turnpike theorems in probabilistic models of economic dynamics

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Abstract

This note is connected with a series of investigations of probabilistic models of economics. Its aim is the study of the asymptotic properties of the optimal programs in such models. The results are the stochastic analogs of the “Turnpike theorems” stating that the optimal programs are near to a definite stationary program for most of the time.

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Literature cited

  1. E. B. Dynkin, “Some probabilistic models for a developing economy,” Dokl. Akad. Nauk SSSR,200, No. 3, 523–525 (1971).

    Google Scholar 

  2. E. B. Dynkin, “Probabilistic concave dynamic programming,” Matem. Sb.,87 (129), No. 4, 490–503 (1972).

    Google Scholar 

  3. E. B. Dynkin, “Optimal programs and stimulating prices in stochastic models of economic growth,” in: Mathematical Models in Economics, PWN-Polish Scientific Publishers, Warszawa (1974), pp. 207–218.

    Google Scholar 

  4. E. B. Dynkin, Stochastic Dynamic Models of an Economic Equilibrium [in Russian], Proceedings of the International Congress of Mathematicians, Vancouver (1974), pp. 757–763.

  5. R. Radner, “Balanced stochastic growth at the maximum rate,” Z. Nationalökonomie, Suppl. No. 1, 39–52 (1971).

    Google Scholar 

  6. R. Radner, “Optimal stationary consumption with stochastic production and resources,” J. Econom. Theory,6, No. 1, 68–90 (1973).

    Google Scholar 

  7. W. A. Brock and L. J. Mirman, “Optimal economic growth and uncertainty: the discounted case,” J. Econom. Theory,4, No. 3, 479–513 (1972).

    Google Scholar 

  8. W. A. Brock and L. J. Mirman, “Optimal economic growth and uncertainty: the no discounting case,“ Int. Econ. Rev.,14, 560–573 (1973).

    Google Scholar 

  9. I. V. Evstigneev, “Optimal economic planning with regard for stationary random factors,” Dokl. Akad. Nauk SSSR,206, No. 5, 1040–1042 (1972).

    Google Scholar 

  10. I. V. Evstigneev, “Asymptotic behavior of optimal programs in stochastic models of economic development,” International Conference on Probability Theory and Mathematical Statistics, Vil'nyus (1973), Theses of Reports, Part I, pp. 219–222.

  11. I. V. Evstigneev, “Optimal stochastic programs and their stimulating prices,” in: Mathematical Models in Economics, PWN-Polish Scientific Publishers, Warszawa (1974), pp. 219–252.

    Google Scholar 

  12. P. A. Samuelson, Efficiency Paths of Capital Accumulation in Terms of the Calculus of Variations, Mathematical Methods in Social Sciences, Stanford Univ. Press, Stanford (1960).

    Google Scholar 

  13. R. Radner, “Paths of economic growth that are optimal with regard only to final states: A turnpike theorem,∝ Rev. Econom. Studies,28, No. 2, 98–104 (1961).

    Google Scholar 

  14. H. Nikaido, “Persistence of continual growth near the von Neumann ray: A strong version of the Radner turnpike theorem,” Econometrica,32, No. 1–2, 151–163 (1964).

    Google Scholar 

  15. J. Tsukui, “Turnpike theorem in a generalized dynamic input-output system,” Econometrica,34, No. 2, 396–407 (1966).

    Google Scholar 

  16. V. L. Makarov and A. M. Rubinov, The Mathematical Theory of Economic Dynamics and Equilibrium [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  17. D. Gale, “A Mathematical theory of optimal economic development,” Bull. Amer. Math. Soc.,74, No. 2, 207–223 (1968).

    Google Scholar 

  18. D. Gale, “On optimal development in a multisector economy,” Rev. Econ. Studies,34, No. 1, 1–18 (1967).

    Google Scholar 

  19. H. Nikaido, Convex Structures and Economic Theory, Academic Press, New York (1968).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 279–290, February, 1976.

The author thanks E. B. Dynkin for useful discussion and help during the preparation of this note.

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Evstigneev, I.V. Turnpike theorems in probabilistic models of economic dynamics. Mathematical Notes of the Academy of Sciences of the USSR 19, 165–171 (1976). https://doi.org/10.1007/BF01098751

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  • DOI: https://doi.org/10.1007/BF01098751

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