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Necessity of Transversality Conditions for Stochastic Problems

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Author Info
Takashi Kamihigashi ()
Abstract

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 further 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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Paper provided by Stony Brook University, Department of Economics in its series Department of Economics Working Papers with number 01-02.

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Date of creation: 2001
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Handle: RePEc:nys:sunysb:01-02

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Related research
Keywords: Transversality condition; stochastic optimization; stochastic reduced-form model; homogeneous returns; stochastic growth model.;

Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
D90 - Microeconomics - - Intertemporal Choice and Growth - - - General
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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  1. Zilcha, Itzhak, 1976. "Characterization by prices of optimal programs under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 173-183, July. [Downloadable!] (restricted)
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  3. Montrucchio, Luigi & Privileggi, Fabio, 1999. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," P.O.L.I.S. department's Working Papers 5, Department of Public Policy and Public Choice - POLIS. [Downloadable!]
    Other versions:
  4. K. Shell, 1968. "Applications of Pontryagin's Maximum Principle of Economics," Working papers 16, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-23, May. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
    Other versions:
  7. Kamihigashi, T., 2001. "A Simple Proof of the Necessity of the Transversality Condition," Discussion Paper Series 116, Research Institute for Economics & Business Administration, Kobe University.
  8. Peleg, Bezalel & Ryder, Harl E, Jr, 1972. "On Optimal Consumption Plans in a Multi-sector Economy," Review of Economic Studies, Blackwell Publishing, vol. 39(2), pages 159-69, April. [Downloadable!] (restricted)
  9. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
    Other versions:
  10. Halkin, Hubert, 1974. "Necessary Conditions for Optimal Control Problems with Infinite Horizons," Econometrica, Econometric Society, vol. 42(2), pages 267-72, March. [Downloadable!] (restricted)
  11. Kamihigashi, Takashi, 2001. "Necessity of Transversality Conditions for Infinite Horizon Problems," Econometrica, Econometric Society, vol. 69(4), pages 995-1012, July.
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  13. 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. [Downloadable!] (restricted)
  14. Takashi Kamihigashi, 1998. "Uniqueness of asset prices in an exchange economy with unbounded utility," Economic Theory, Springer, vol. 12(1), pages 103-122. [Downloadable!] (restricted)
  15. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November. [Downloadable!] (restricted)
  16. 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. [Downloadable!] (restricted)
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