Workgroup Financial Mathematics

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Risk Preferences and their Robust Representation (Michael Kupper)


Due to the plurality of interpretations of risk, we concentrate on context invariant features related to this notion: diversification and monotonicity. We define and study general properties of three key concepts, risk order, risk measure and risk acceptance family and their one-to-one relations. Our main result is a uniquely characterized dual robust representation of lower semi continuous risk orders. We then illustrate this approach in different settings. In the setup of random variables, where risk perception can be interpreted as a model risk, we give a robust representation for numerous risk measures: various certainty equivalents, or a general version of Aumann and Serrano's economic index. In the setup of lotteries where risk perception can be seen as a distributional risk, we show that the Value at Risk is a risk measure on this level (not for random variables) and give a robust representation. Finally risk perception on state dependent lotteries à la Anscombe and Aumann, where results clarifying the interplay between model risk and distributional risk are given, in particular for the Cerreia-Vioglio, Maccheroni, Marinacci, and Montrucchio uncertainty preferences. It is based on joint work with Samuel Drapeau.