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Necessity of Transversality Conditions for Stochastic Problems

  • Takashi Kamihigashi

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

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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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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  1. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-72, March.
  2. Woodford, Michael & Santos, Manuel S., 1995. "Rational asset pricing bubbles," UC3M Working papers. Economics 3913, Universidad Carlos III de Madrid. Departamento de Economía.
  3. Montrucchio, Luigi & Privileggi, Fabio, 1999. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," POLIS Working Papers 5, Institute of Public Policy and Public Choice - POLIS.
  4. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
  5. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  6. Takashi Kamihigashi, 2000. "Necessity of Transversality Conditions for Stochastic Problems," Discussion Paper Series 115, Research Institute for Economics & Business Administration, Kobe University.
  7. Sergio Rebelo, 1999. "Long Run Policy Analysis and Long Run Growth," Levine's Working Paper Archive 2114, David K. Levine.
  8. Martin L. Weitzman, 1973. "Duality Theory for Infinite Horizon Convex Models," Management Science, INFORMS, vol. 19(7), pages 783-789, March.
  9. Takashi Kamihigashi, 2000. "A simple proof of Ekeland and Scheinkman's result on the necessity of a transversality condition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 463-468.
  10. 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.
  11. 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.
  12. 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.
  13. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  14. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 275-280.
  15. Zilcha, Itzhak, 1978. "Transversality Condition in a Multi-Sector Economy under Uncertainty," Econometrica, Econometric Society, vol. 46(3), pages 515-25, May.
  16. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  17. Bezalel Peleg & Harl E. Ryder, 1972. "On Optimal Consumption Plans in a Multi-sector Economy," Review of Economic Studies, Oxford University Press, vol. 39(2), pages 159-169.
  18. Takashi Kamihigashi, 1998. "Uniqueness of asset prices in an exchange economy with unbounded utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 103-122.
  19. 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.
  20. 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.
  21. Zilcha, Itzhak, 1976. "Characterization by prices of optimal programs under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 173-183, July.
  22. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-23, May.
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