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Transversality Conditions for Stochastic Higher-Order Optimality: Continuous and Discrete Time Problems

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  • Dapeng Cai
  • Takashi Gyoshin Nitta

Abstract

Higher-order optimization problems naturally appear when investigating the effects of a patent with finite length, as in the pioneering work of Futagami and Iwaisako (2007). In this paper, we establish the Euler equations and transversality conditions necessary for analyzing such higher-order optimization problems. We develop our results for stochastic general reduced-form models and consider cases of both continuous and discrete time. We employ our results to establish the Euler equations and transversality conditions for the simplified household maximization problem in Futagami and Iwaisako (2007).

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  • Dapeng Cai & Takashi Gyoshin Nitta, 2012. "Transversality Conditions for Stochastic Higher-Order Optimality: Continuous and Discrete Time Problems," Papers 1203.3869, arXiv.org.
    • Handle: RePEc:arx:papers:1203.3869
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    References listed on IDEAS

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    1. Takashi Kamihigashi, 2002. "A simple proof of the necessity of the transversality condition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 427-433.
    2. Kamihigashi, Takashi, 2003. "Necessity of transversality conditions for stochastic problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 140-149, March.
    3. 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.
    4. Dapeng Cai & Takashi Gyoshin Nitta, 2010. "Transversality Conditions for Higher Order Infinite Horizon Discrete Time Optimization Problems," Papers 1004.3093, arXiv.org.
    5. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-723, May.
    6. Futagami, Koichi & Iwaisako, Tatsuro, 2007. "Dynamic analysis of patent policy in an endogenous growth model," Journal of Economic Theory, Elsevier, vol. 132(1), pages 306-334, January.
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    Cited by:

    1. Christian Kiedaisch, 2021. "Growth and welfare effects of intellectual property rights when consumers differ in income," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1121-1170, November.

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