Previous |  Up |  Next


Title: Stable solutions to homogeneous difference-differential equations with constant coefficients: Analytical instruments and an application to monetary theory (English)
Author: von Kalckreuth, Ulf
Author: Krtscha, Manfred
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 49
Issue: 4
Year: 2004
Pages: 373-386
Summary lang: English
Category: math
Summary: In economic systems, reactions to external shocks often come with a delay. On the other hand, agents try to anticipate future developments. Both can lead to difference-differential equations with an advancing argument. These are more difficult to handle than either difference or differential equations, but they have the merit of added realism and increased credibility. This paper generalizes a model from monetary economics by von Kalckreuth and Schröder. Working out its stability properties, we present a general method for determining the stability of any solution to a homogeneous linear difference-differential equation with constant coefficients and advancing arguments. (English)
Keyword: linear difference-differential equations
Keyword: stability
Keyword: monetary transmission
MSC: 34K06
MSC: 39A11
MSC: 39B99
MSC: 91B02
MSC: 91B62
MSC: 91B64
idZBL: Zbl 1099.39009
idMR: MR2076491
DOI: 10.1007/s10492-004-6405-y
Date available: 2009-09-22T18:18:41Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] R. Bellman, K. L. Cooke: Differential-Difference Equations.Academic Press, New York-London, 1963. MR 0147745
Reference: [2] R.  Dornbusch: Expectation and exchange rate dynamics.Journal of Political Economics 84 (1976), 1161–1176. 10.1086/260506
Reference: [3] R. D.  Driver: Ordinary and Delay Differential Equations.Springer-Verlag, New York-Heidelberg-Berlin, 1997. MR 0477368
Reference: [4] J. K.  Hale, S. M.  Verduyn Lunel: Introduction to Functional Differential Equations.Springer-Verlag, New York, 1993. MR 1243878
Reference: [5] W. H.  Fisher, S. J.  Turnovsky: Fiscal policy and the term structure of interest rates: an intertemporal analysis.Journal of Money, Credit and Banking 24 (1992), 1–26. 10.2307/1992788
Reference: [6] M. R.  Gray, S. J. Turnovsky: The stability of exchange rate dynamics under perfect myopic foresight.Int. Econ. Rev. 20 (1979), 643–660. 10.2307/2526263
Reference: [7] A.  de la Fuente: Mathematical Methods and Models for Economists.Cambridge University Press, Cambridge, 2000. Zbl 0943.91001, MR 1735968
Reference: [8] K. P.  Hadeler: Mathematik für Biologen.Springer-Verlag, Heidelberg, 1974. Zbl 0286.92001, MR 0411289
Reference: [9] E. Hilb: Zur Theorie der linearen funktionalen Differentialgleichungen.Math. Ann. 78 (1918), 137–170. MR 1511888
Reference: [10] U.  von Kalckreuth, J.  Schröder: Monetary transmission in the new economy: service life of capital, transmission channels and the speed of adjustment.Jahrbuch für Wirtschaftswissenschaften (Review of Economics) 53 (2002), 125–141.
Reference: [11] M. Krtscha: Short-term and long-term interest rates in a monetary model of a closed economy.Operations Research  91, Physica Verlag Heidelberg, 1991.
Reference: [12] M.  Krtscha: The dependence of the price level on the expansion of the money supply in closed economies.Mathematical Modelling in Economics, Springer-Verlag, Berlin, 1993, pp. 249–259. Zbl 0849.90030
Reference: [13] J. H.  McCulloch: Measuring the term structure of interest rates.The Journal of Business 44 (1971), 19–31. 10.1086/295329
Reference: [14] T.  Sargent, N.  Wallace: The stability of models of money and growth with perfect foresight.Econometrica 41 (1973), 1043–1048. 10.2307/1914034
Reference: [15] C. A.  Wilson: Anticipated shocks and exchange rate dynamics.Journal of Political Economicy 87 (1979), 639–647. 10.1086/260782


Files Size Format View
AplMat_49-2004-4_5.pdf 1.570Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo