Optimal growth in a two-sector economy facing an expected random shock. (English) Zbl 1308.91109

Proc. Steklov Inst. Math. 276, Suppl. 1, S4-S34 (2012) and Tr. Inst. Mat. Mekh. (Ekaterinburg) 17, No. 2, 271-299 (2011).
This article deals with an optimal growth in the two-sector model with two kind of technologies (“clean” and “dirty”). The growth of each sector is described by the system of linear differential equations. It is assumed that in some random time the parameters of the equation change while the moment of the change has an exponential distribution. The problem of optimizing the social welfare function is stated as the optimal control problem and solved using Pontryagin’s maximum principle. The authors give a characterization of the solutions for all possible cases (relations of the values of parameters). The analysis is performed by the qualitative analysis of differential equations: phase diagrams and checking vector fields generated by the system.


91B62 Economic growth models
91B55 Economic dynamics
91B66 Multisectoral models in economics
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
49N90 Applications of optimal control and differential games
Full Text: DOI


[1] P. Aghion and P. Howitt, Endogenous Growth Theory (MIT Press, Cambridge, MA, 1998). · Zbl 0927.91015
[2] V. I. Arnold, Supplementary Chapters to the Theory of Ordinary Differential Equations (Nauka, Moscow, 1978) [in Russian].
[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.
[4] S. M. Aseev and A. V. Kryazhimskii, Proc. Steklov Inst. Math. 257(1), 1 (2007). · Zbl 1215.49001
[5] R. J. Barro and X. Sala-i-Martin, Economic Growth (McGraw Hill, New York, 1995).
[6] R. Gabasov and F. M. Kirillova, Singular Optimal Control (Plenum, New York, 1982). · Zbl 0211.18401
[7] B. V. Gnedenko, Theory of Probability (Gordon & Breach, Newark, NJ, 1997).
[8] P. Hartman, Ordinary Differential Equations (Wiley, New York, 1964). · Zbl 0125.32102
[9] L. S. Pontryagin, V. G. Boltyanski, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Pergamon, Oxford, 1964).
[10] K. Wälde, J. Econom. Dynam. Control 27, 1 (2002). · Zbl 1009.91049
[11] K. Wälde, in Stochastic Economic Dynamics, Ed. by B. S. Jensen and T. Palokangas (Copenhagen Business School, Frederiksberg, 2007), pp. 393–422.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.