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Stochastic Control, Optimal Saving, and Job Search in Continuous Time

Economic uncertainty may affect significantly people’s behavior and hence macroeconomic variables. It is thus important to understand how people behave in presence of different kinds of economic risk. The present dissertation focuses therefore on the impact of the uncertainty in capital and labor income on the individual saving behavior. The underlying uncertain variables are here modeled as stochastic processes that each obey a specific stochastic differential equation, where uncertainty stems either from Poisson or Lévy processes. The results on the optimal behavior are derived by maximizing the individual expected lifetime utility. The first chapter is concerned with the necessary mathematical tools, the change-of-variables formula and the Hamilton-Jacobi-Bellman equation under Poisson uncertainty. We extend their possible field of application in order make them appropriate for the analysis of the dynamic stochastic optimization problems occurring in the following chapters and elsewhere. The second chapter considers an optimum-saving problem with labor income, where capital risk stems from asset prices that follow geometric L´evy processes. Chapter 3, finally, studies the optimal saving behavior if agents face not only risk but also uncertain spells of unemployment. To this end, we turn back to Poisson processes, which here are used to model properly the separation and matching process.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:23974
Date13 November 2007
CreatorsSennewald, Ken
ContributorsWälde, Klaus, Broll, Udo, Schwödiauer, Gerhard
PublisherTechnische Universität Dresden
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

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