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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 establishes (i) an extension of Michel's (1990, Theorem 1) necessity result to an abstract reduced-form model, (ii) a generalization of the results of Weitzman (1973) and Ekeland and Scheinkman (1986), and (iii) a new result that is useful particularly in the case of homogeneous returns. These results are shown for an extremely general discrete-time reduced-form model that does not assume differentiability, continuity, or concavity, and that imposes virtually no restriction on the state spaces. The three results are futher extended to a stochastic reduced-form model. The stochastic extensions are easily accomplished since our deterministic model is so general that the stochastic model is in fact a special case of the deterministic model. We apply our stochastic results to a stochastic reduced-form model with homogeneous returns and a general type of stochastic growth model with CRRA utility.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/dp115.pdf
File Function: First version, 2000
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Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number 115.

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Length: 25 pages
Date of creation: Nov 2000
Date of revision:
Handle: RePEc:kob:dpaper:115
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  1. 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.
  2. Takashi Kamihigashi, 2002. "A simple proof of the necessity of the transversality condition," Economic Theory, Springer, vol. 20(2), pages 427-433.
  3. Zilcha, Itzhak, 1978. "Transversality Condition in a Multi-Sector Economy under Uncertainty," Econometrica, Econometric Society, vol. 46(3), pages 515-25, May.
  4. 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.
  5. 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.
  6. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
  7. Takashi Kamihigashi, 1998. "Uniqueness of asset prices in an exchange economy with unbounded utility," Economic Theory, Springer, vol. 12(1), pages 103-122.
  8. Zilcha, Itzhak, 1976. "Characterization by prices of optimal programs under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 173-183, July.
  9. 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.
  10. Martin L. Weitzman, 1973. "Duality Theory for Infinite Horizon Convex Models," Management Science, INFORMS, vol. 19(7), pages 783-789, March.
  11. 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.
  12. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
  13. 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.
  14. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-23, May.
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