TY - JOUR
T1 - Convex risk measures on Orlicz spaces
T2 - Inf-convolution and shortfall
AU - Arai, Takuji
N1 - Funding Information:
Acknowledgements This research was supported by Scientific Research (C) No.19540144 from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The author would like to thank Martin Schweizer for his valuable comments and suggestions.
PY - 2010/7
Y1 - 2010/7
N2 - 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.
AB - 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.
KW - Convex risk measure
KW - Inf-convolution
KW - Orlicz space
KW - Shortfall
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U2 - 10.1007/s11579-010-0028-8
DO - 10.1007/s11579-010-0028-8
M3 - Article
AN - SCOPUS:77953913299
SN - 1862-9679
VL - 3
SP - 73
EP - 88
JO - Mathematics and Financial Economics
JF - Mathematics and Financial Economics
IS - 2
ER -