Optimization of Convex Risk Functions
Mathematics of Operations Research
Complete Monotone Quasiconcave Duality
Mathematics of Operations Research
Aspirational Preferences and Their Representation by Risk Measures
Management Science
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To address the plurality of interpretations of the subjective notion of risk, we describe it by means of a risk order and concentrate on the context invariant features of diversification and monotonicity. Our main results are uniquely characterized robust representations of lower semicontinuous risk orders on vector spaces and convex sets. This representation covers most instruments related to risk and allows for a differentiated interpretation depending on the underlying context that is illustrated in different settings: for random variables, risk perception can be interpreted as model risk, and we compute among others the robust representation of the economic index of riskiness. For lotteries, risk perception can be viewed as distributional risk and we study the “value at risk.” For consumption patterns, which excerpt an intertemporality dimension in risk perception, we provide an interpretation in terms of discounting risk and discuss some examples.