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Convex risk measures on Orlicz spaces: inf-convolution and shortfall

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Abstract

We focus on, throughout this paper, convex risk measures defined on Orlicz spaces. In particular, we investigate basic properties of inf-convolutions defined between a convex risk measure and a convex set, and between two convex risk measures. Moreover, we study shortfall risk measures, which are convex risk measures induced by the shortfall risk. By using results on inf-convolutions, we obtain a robust representation result for shortfall risk measures defined on Orlicz spaces under the assumption that the set of hedging strategies has the sequential compactness in a weak sense. We discuss in addition a construction of an example having the sequential compactness.

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Correspondence to Takuji Arai.

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Arai, T. Convex risk measures on Orlicz spaces: inf-convolution and shortfall. Math Finan Econ 3, 73–88 (2010). https://doi.org/10.1007/s11579-010-0028-8

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  • DOI: https://doi.org/10.1007/s11579-010-0028-8

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