Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/191422
Authors: 
Bayer, Christian
Rendall, Alan D.
Wälde, Klaus
Year of Publication: 
2018
Series/Report no.: 
CESifo Working Paper No. 7397
Abstract: 
We study optimal savings in continuous time with exogenous transitions between employment and unemployment as the only source of uncertainty in a small open economy. We prove the existence of an optimal consumption path. We exploit that the dynamics of consumption and wealth between jumps can be expressed as a Fuchsian system. We derive conditions under which an invariant joint distribution for the state variables, i.e., wealth and labour market status, exists and is unique. We also provide conditions under which the distribution of these variables converges to the invariant distribution. Our analysis relies on the notion of T-processes and applies results on the stability of Markovian processes from Meyn and Tweedie (1993a, b,c).
Subjects: 
uncertainty in continuous time
counting process
existence
uniqueness
stability
JEL: 
C62
D91
J63
Document Type: 
Working Paper

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