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Necessity of Transversality Conditions for Infinite Horizon Problems

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Author Info
Kamihigashi, Takashi
Abstract

This paper studies necessity of transversality conditions for the continuous time, reduced form model. By generalizing Benveniste and Scheinkman's (1982) "envelope" condition and Michel's (1990) version of the squeezing argument, we show a generalization of Michel's (1990, Theorem 1) necessity result that does not assume concavity. The generalization enables us to generalize Ekeland and Scheinkman's (1986) result as well as to establish a new result that does not require the objective functional to be finite. The new result implies that homogeneity of the return function alone is sufficient for the necessity of the most standard transversality condition. Our results are also applied to a nonstationary version of the one-sector growth model. It is shown that bubbles never arise in an equilibrium asset pricing model with a nonlinear constraint.

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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 69 (2001)
Issue (Month): 4 (July)
Pages: 995-1012
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Handle: RePEc:ecm:emetrp:v:69:y:2001:i:4:p:995-1012

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  1. Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Constructing the Optimal Solutions to the Undiscounted Continuous-Time Infinite Horizon Optimization Problems," Quantitative Finance Papers 0803.4046, arXiv.org. [Downloadable!]
  2. Takashi Kamihigashi, 2003. "Necessity of the Transversality Condition for Stochastic Models with CRRA Utility," Discussion Paper Series 137, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
  3. Dapeng CAI & Takashi Gyoshin NITTA, 2008. "Limit of the Solutions for the Finite Horizon Problems as the Optimal Solution to the Infinite Horizon Optimization Problems," Quantitative Finance Papers 0803.4050, arXiv.org. [Downloadable!]
  4. Takashi Kamihigashi, 2004. "Necessity of the Transversality Condition for Stochastic Models with Bounded or CRRA Utility," Discussion Paper Series 152, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
  5. LE VAN, Cuong & BOUCEKKINE, Raouf & SAGLAM, Cagri, 2004. "Optimal control in infinite horizon problems: A Sobolev space approach," CORE Discussion Papers 2004089, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
    Other versions:
  6. Hsieh Hsih-chia & Hsieh Pei-gin, 2004. "A Generalized Theory of Monetary and Macroeconomics," Money Macro and Finance (MMF) Research Group Conference 2004 50, Money Macro and Finance Research Group. [Downloadable!]
  7. Takashi Kamihigashi, 2004. "Necessity of the Transversality Condition for Stochastic Models with Bounded or CRRA Utility," Discussion Paper Series 162, Research Institute for Economics & Business Administration, Kobe University, revised Oct 2004. [Downloadable!]
  8. Takashi Kamihigashi, 2007. "The Spirit of Capitalism, Stock Market Bubbles, and Output Fluctuations," Discussion Paper Series 205, Research Institute for Economics & Business Administration, Kobe University, revised Oct 2007. [Downloadable!]
  9. Takashi Kamihigashi, 2006. "Transversality Conditions and Dynamic Economic Behavior," Discussion Paper Series 180, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
  10. Buiter, Willem H, 2004. "Helicopter Money: Irredeemable Fiat Money and the Liquidity Trap," CEPR Discussion Papers 4202, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  11. Takashi Kamihigashi, 2001. "Necessity of Transversality Conditions for Stochastic Problems," Department of Economics Working Papers 01-02, Stony Brook University, Department of Economics. [Downloadable!]
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