Optimal growth in a two-sector economy facing an expected random shock



We develop an optimal growth model of an open economy that uses both an old (“dirty” or “polluting”) technology and a new (“clean”) technology simultaneously. A planner of the economy expects the occurrence of a random shock that increases sharply abatement costs in the dirty sector. Assuming that the probability of an exogenous environmental shock is distributed according to the exponential law, we use Pontryagin’s maximum principle to find the optimal investment and consumption policies for the economy.


dynamic optimization optimal control Pontryagin’s maximum principle endogenous growth climate change random shock government policy technological development 


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  1. 1.
    P. Aghion and P. Howitt, Endogenous Growth Theory (MIT Press, Cambridge, MA, 1998).Google Scholar
  2. 2.
    V. I. Arnold, Supplementary Chapters to the Theory of Ordinary Differential Equations (Nauka, Moscow, 1978) [in Russian].Google Scholar
  3. 3.
    S. Aseev, K. Besov, S.-E. Ollus, and T. Palokangas, in Dynamic Systems, Economic Growth, and the Environment, Ed. by J. C. Cuaresma, T. Palokangas, and A. Tarasyev (Springer-Verlag, Berlin, 2010), Ser. Dynamic Modeling and Econometrics in Economics and Finance, Vol. 12, pp. 109–137.CrossRefGoogle Scholar
  4. 4.
    S. M. Aseev and A. V. Kryazhimskii, Proc. Steklov Inst. Math. 257(1), 1 (2007).MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    R. J. Barro and X. Sala-i-Martin, Economic Growth (McGraw Hill, New York, 1995).Google Scholar
  6. 6.
    R. Gabasov and F. M. Kirillova, Singular Optimal Control (Plenum, New York, 1982).Google Scholar
  7. 7.
    B. V. Gnedenko, Theory of Probability (Gordon & Breach, Newark, NJ, 1997).MATHGoogle Scholar
  8. 8.
    P. Hartman, Ordinary Differential Equations (Wiley, New York, 1964).MATHGoogle Scholar
  9. 9.
    L. S. Pontryagin, V. G. Boltyanski, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Pergamon, Oxford, 1964).MATHGoogle Scholar
  10. 10.
    K. Wälde, J. Econom. Dynam. Control 27, 1 (2002).MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    K. Wälde, in Stochastic Economic Dynamics, Ed. by B. S. Jensen and T. Palokangas (Copenhagen Business School, Frederiksberg, 2007), pp. 393–422.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • S. Aseev
    • 1
    • 2
  • K. Besov
    • 3
  • S. -E. Ollus
    • 4
  • T. Palokangas
    • 5
  1. 1.Steklov Mathematical Institute of the Russian Academy of SciencesMoscowRussia
  2. 2.International Institute for Applied Systems AnalysisLaxenburgAustria
  3. 3.Steklov Mathematical Institute of the Russian Academy of SciencesMoscowRussia
  4. 4.Fortum CorporationFortumFinland
  5. 5.Helsinki Center of Economic ResearchUniversity of HelsinkiHelsinkiFinland

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