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

Hippolyte D'Albis 1, 2, Emmanuelle Augeraud-Véron 3, Hermen Jan Hupkes 4

(2012-06)

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:	Ecole d'Économie de Paris - Paris School of Economics (EEP-PSE)
	Ecole d'Économie de Paris
2:	Centre d'économie de la Sorbonne (CES)
	CNRS : UMR8174 – Université Paris I - Panthéon-Sorbonne
3:	Mathématiques, Image et Applications (MIA)
	Université de La Rochelle : EA3165
4:	University of Missouri - Columbia
	Mathematics Department

Research team: Axe Macroéconomie

Subject

:

Humanities and Social Sciences/Economy and finances Mathematics/Functional Analysis

Keyword(s): Functional differential equations – advanced and retarded arguments – interest rates – inflation rates – initial value problems – indeterminacy – impulsive equations.

halshs-00717412, version 1

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From: Lucie Label <>

Submitted on: Thursday, 12 July 2012 16:49:35

Updated on: Friday, 13 July 2012 11:01:18