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Discontinuous Initial Value Problems for Funtional Differential-Algebraic Equations of Mixed Type

Hippolyte D'Albis1, 2, Emmanuelle Augeraud-Véron3, Hermen Jan Hupkes4

We study the well-posedness of initial value problems for nonlinear functional differential-algebraic equations of mixed type. We are interested in solutions to such problems that admit a single jump discontinuity at time zero. We focus specially on the question whether unstable equilibria can be stabilized by appropriately choosing the size of the jump discontinuity. We illustrate our techniques by analytically studying an economic model for the interplay between inflation and interest rates. In particular, we investigate under which circumstances the central bank can prevent runaway inflation by appropriately hiking the interest rate.

1 :	EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics
2 :	CES - Centre d'économie de la Sorbonne
3 :	MIA - Mathématiques, Image et Applications
4 :	University of Missouri - Columbia

Équipe de recherche : Axe Macroéconomie

Mots-Clés : Functional differential equations – advanced and retarded arguments – interest rates – inflation rates – initial value problems – indeterminacy – impulsive equations.

halshs-00717412, version 1

http://halshs.archives-ouvertes.fr/halshs-00717412

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Contributeur : Lucie Label <>

Soumis le : Jeudi 12 Juillet 2012, 16:49:35

Dernière modification le : Vendredi 13 Juillet 2012, 11:01:18