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Asymptotic Growth under Uncertainty: Existence and Uniqueness

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  • Fwu-Ranq Chang
  • A. G. Malliaris

Abstract

This paper demonstrates, using the Reflection Principle, the existence and uniqueness of the solution to the classic Solow equation under continuous time uncertainty for the class of strictly concave production functions which are continuously differentiable on the nonnegative real numbers. This class contains all CES functions with elasticity of substitution less than unity. A steady state distribution also exists for this class of production functions which have a bounded slope at the origin. A condition on the drift-variance ratio of the stochastic differential equation alone, independent of technology and the savings ratio, is found to be necessary for the existence of a steady state.

Suggested Citation

  • Fwu-Ranq Chang & A. G. Malliaris, 1987. "Asymptotic Growth under Uncertainty: Existence and Uniqueness," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 169-174.
    • Handle: RePEc:oup:restud:v:54:y:1987:i:1:p:169-174.
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    Cited by:

    1. Darong Dai, 2014. "A Golden Formula in Neoclassical-Growth Models with Brownian-Motion Shocks," Scottish Journal of Political Economy, Scottish Economic Society, vol. 61(2), pages 211-228, May.
    2. Christian Bayer & Klaus Waelde, 2011. "Existence, Uniqueness and Stability of Invariant Distributions in Continuous-Time Stochastic Models," Working Papers 1111, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 21 Jul 2011.
    3. Joshi, Sumit, 1998. "A framework to analyze comparative dynamics in a continuous time stochastic growth model," Economic Modelling, Elsevier, vol. 15(1), pages 125-134, January.
    4. Bayer, Christian & Rendall, Alan D. & Wälde, Klaus, 2019. "The invariant distribution of wealth and employment status in a small open economy with precautionary savings," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 17-37.
    5. Dai, Darong, 2012. "A Robust Turnpike Deduced by Economic Maturity," MPRA Paper 48818, University Library of Munich, Germany.
    6. Darong Dai, 2015. "Robust Turnpikes Deduced by the Minimum-Time Needed toward Economic Maturity," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(1), pages 049-073, October.
    7. Leong, Chee Kian & Huang, Weihong, 2010. "A stochastic differential game of capitalism," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 552-561, July.
    8. Gilles Dufrénot & Anne-Charlotte Paret Onorato, 2016. "Power-Law Distribution in the Debt-to-Fiscal Revenue Ratio: Empirical Evidence and a Theoretical Model," AMSE Working Papers 1627, Aix-Marseille School of Economics, France.
    9. Bjarne S. Jensen & Martin Richter, 2008. "Stochastic One-Sector and Two-Sector Growth Models in Continuous Time," DEGIT Conference Papers c013_035, DEGIT, Dynamics, Economic Growth, and International Trade.
    10. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    11. Dai, Darong, 2012. "Comparative Studies on Cooperative Stochastic Differential Game and Dynamic Sequential Game of Economic Maturity," MPRA Paper 44339, University Library of Munich, Germany.
    12. Wu, Fuke & Mao, Xuerong & Yin, Juliang, 2008. "Uncertainty and economic growth in a stochastic R&D model," Economic Modelling, Elsevier, vol. 25(6), pages 1306-1317, November.
    13. Behrens, Axel, 1990. "Optimal growth under stochastic resource supply," Kiel Working Papers 438, Kiel Institute for the World Economy (IfW Kiel).

    More about this item

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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