Dual characterization of properties of risk measures on Orlicz hearts |
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Authors: | Patrick Cheridito Tianhui Li |
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Institution: | (1) Princeton University, Princeton, NJ 08544, USA;(2) Cambridge University, Cambridge, CB3 0DS, UK |
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Abstract: | We extend earlier representation results for monetary risk measures on Orlicz
hearts. Then we give general conditions for such risk measures to be Gateaux-differentiable,
strictly monotone with respect to almost sure inequality, strictly convex modulo translation,
strictly convex modulo comonotonicity, or monotone with respect to different stochastic
orders. The theoretical results are used to analyze various specific examples of risk measures.
We thank Andreas Hamel and Michael Kupper for fruitful discussions and helpful comments. P. Cheridito has been supported by
NSF Grant DMS-0642361, a Rheinstein Award and a Peek Fellowship. T. Li has been supported by a Marshall Scholarship and a
Merage Fellowship. |
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Keywords: | Risk measures Gateaux-differentiability Strict monotonicity Strict convexity Stochastic orders Orlicz hearts |
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