Risk preferences and their robust representation [Elektronische Ressource] / von Samuel Drapeau

Risk Preferences and their Robust RepresentationDISSERTATIONzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. Rer. Nat.)im Fach Mathematikeingereicht an derMathematisch-Wissenschaftlichen Fakultät IIHumboldt-Universität zu BerlinvonHerrn Dipl.-Math. Samuel Drapeaugeboren am 23.05.1977 in Sablé sur SarthePräsident der Humboldt-Universität zu Berlin:Prof. Dr. Dr. h.c. Christoph MarkschiesDekan der Mathematisch-Wissenschaftlichen Fakultät II:Prof. Dr. sc. Peter FrenschGutachter:1. Prof. Dr. Hans Föllmer2. Prof. Dr. Michael Kupper3. Prof. Dr. Frank Riedeleingereicht am: 15.02.2010Tag der mündlichen Prüfung: 30.04.2010AbstractThe goal of this thesis is the conceptual study of risk and its quantification viarobust representations.In a first part, we consider risk within a context which extends the notion of“measurable uncertainty” introduced by Frank Knight [1921]. Mathematically,the risk perception of risky elements in a convex setX is expressed by a pref-erence order< having the properties of quasiconvexity and monotonicity. Theseproperties are the appropriate translation of the two consensual statements that“diversification should not increase the risk” and “the better for sure, the lessrisky”. Such a preference order will be called a risk order. We keep full latitudeon the choice of the underlying setting and thus leave room for different interpre-tations of risk.