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Necessity of Transversality Conditions for Stochastic Problems

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  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

Abstract

This paper shows stochastic versions of (i) Michel's (1990, Econometrica 58, 705--723, Theorem 1) necessity result , (ii) a generalization of the TVC results of Weitzman (1973, Manage. Sci. 19, 783--789) and Ekeland and Scheinkman (1986, Math. Oper. Res. 11, 216--229), and (iii) Kamihigashi's (2001, Econometrica 69, 995--1012, Theorem 3.4) result, which is useful particularly in the case of homogeneous returns. These stochastic extensions are established for an extremely general stochastic reduced-form model that assumes neither differentiability nor continuity.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp128.pdf
File Function: First version, 2002
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Bibliographic Info

Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 128.

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Length: 12 pages
Date of creation: Apr 2002
Date of revision:
Handle: RePEc:kob:dpaper:128

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Keywords: Transversality condition; Stochastic optimization; Stochastic reduced-form model; Homogeneous returns; Stochastic growth model;

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  1. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
  2. Brock, William A, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Wiley Blackwell, vol. 37(2), pages 275-80, April.
  3. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  4. Takashi Kamihigashi, 2000. "A simple proof of Ekeland and Scheinkman's result on the necessity of a transversality condition," Economic Theory, Springer, vol. 15(2), pages 463-468.
  5. Montrucchio, Luigi & Privileggi, Fabio, 2001. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," Journal of Economic Theory, Elsevier, vol. 101(1), pages 158-188, November.
  6. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-23, May.
  7. Takashi Kamihigashi, 2002. "A simple proof of the necessity of the transversality condition," Economic Theory, Springer, vol. 20(2), pages 427-433.
  8. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
  9. Zilcha, Itzhak, 1976. "Characterization by prices of optimal programs under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 173-183, July.
  10. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  11. Zilcha, Itzhak, 1978. "Transversality Condition in a Multi-Sector Economy under Uncertainty," Econometrica, Econometric Society, vol. 46(3), pages 515-25, May.
  12. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
  13. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  14. Takekuma, Shin-Ichi, 1992. "Optimal Growth under Uncertainty: A Complete Characterization of Weakly Maximal Programs," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 33(2), pages 169-182, December.
  15. Yano, Makoto, 1989. "Comparative statics in dynamic stochastic models : Differential analysis of a stochastic modified golden rule state in a banach space," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 169-185, April.
  16. Peleg, Bezalel & Ryder, Harl E, Jr, 1972. "On Optimal Consumption Plans in a Multi-sector Economy," Review of Economic Studies, Wiley Blackwell, vol. 39(2), pages 159-69, April.
  17. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  18. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-72, March.
  19. Takashi Kamihigashi, 2001. "A Simple Proof of the Necessity of the Transversality Condition," Discussion Paper Series 116, Research Institute for Economics & Business Administration, Kobe University.
  20. Martin L. Weitzman, 1973. "Duality Theory for Infinite Horizon Convex Models," Management Science, INFORMS, vol. 19(7), pages 783-789, March.
  21. Takashi Kamihigashi, 1998. "Uniqueness of asset prices in an exchange economy with unbounded utility," Economic Theory, Springer, vol. 12(1), pages 103-122.
  22. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  23. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
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