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On Dynamic Coherent and Convex Risk Measures
Risk Optimal Behavior and Information Gains

dc.contributor.advisorRiedel, Frank
dc.contributor.authorEngelage, Daniel
dc.description.abstractWe consider tangible economic problems for agents assessing risk by virtue of dynamic coherent and convex risk measures or, equivalently, utility in terms of dynamic multiple priors and dynamic variational preferences in an uncertain environment.
Solutions to the Best-Choice problem for a risky number of applicants are well-known. In Chapter 2, we set up a model with an ambiguous number of applicants when the agent assess utility with multiple prior preferences. We achieve a solution by virtue of multiple prior Snell envelopes for a model based on so called assessments. The main result enhances us with conditions for the ambiguous problem to possess finitely many stopping islands.
In Chapter 3 we consider general optimal stopping problems for an agent assessing utility by virtue of dynamic variational preferences. Introducing variational supermartingales and an accompanying theory, we obtain optimal solutions for the stopping problem and a minimax result. To illustrate, we consider prominent examples: dynamic entropic risk measures and a dynamic version of generalized average value at risk.
In Chapter 4, we tackle the problem how anticipation of risk in an uncertain environment changes when information is gathered in course of time. A constructive approach by virtue of the minimal penalty function for dynamic convex risk measures reveals time-consistency problems. Taking the robust representation of dynamic convex risk measures as given, we show that all uncertainty is revealed in the limit, i.e. agents behave as expected utility maximizers given the true underlying distribution. This result is a generalization of the fundamental Blackwell-Dubins theorem showing coherent as well as convex risk measures to merge in the long run.
dc.rightsIn Copyright
dc.subjectDynamische Variationspräferenzen
dc.subjectDynamische Multiple-Prior-Präferenzen
dc.subjectDynamische Konvexe Risikomaße
dc.subjectDynamische Kohärente Risikomaße
dc.subjectDynamische Straffunktion
dc.subjectOptimales Stoppen
dc.subjectSatz von Blackwell und Dubins
dc.subjectDynamic Variational Preferences
dc.subjectDynamic Multiple Prior Preferences
dc.subjectDynamic Convex Risk Measures
dc.subjectDynamic Coherent Risk Measures
dc.subjectDynamic Penalty
dc.subjectBest-Choice Problem
dc.subjectOptimal Stopping
dc.subjectBlackwell-Dubins Theorem
dc.subject.ddc330 Wirtschaft
dc.titleOn Dynamic Coherent and Convex Risk Measures
dc.title.alternativeRisk Optimal Behavior and Information Gains
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.fakultaetRechts- und Staatswissenschaftliche Fakultät
dc.contributor.coRefereeLütkebohmert-Holtz, Eva

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