Journal
MATHEMATICS OF OPERATIONS RESEARCH
Volume 38, Issue 1, Pages 28-62Publisher
INFORMS
DOI: 10.1287/moor.1120.0560
Keywords
risk perception; risk measures; robustness
Funding
- MATHEON project [E.11]
- Berlin Mathematical School
- DFG [IRTG 1339]
- Vienna Science and Technology Fund
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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.
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