Convex risk measures on Orlicz spaces: inf-convolution and shortfall
Convex risk measures on Orlicz spaces: inf-convolution and shortfall
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DOI：
10.1007/s11579-010-0028-8
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发表时间：
2010-05
影响因子：
1.6
通讯作者：
Takuji Arai
中科院分区：
文献类型：
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作者：
Takuji Arai
我们专注于，在整个本文中，凸风险度量定义在Orlicz空间。特别是，我们调查的基本性质的下卷积定义之间的凸风险措施和凸集，和两个凸风险措施。此外，我们还研究了缺口风险测度，这是由缺口风险引起的凸风险测度。利用下卷积的结果，在套期保值策略集具有弱序列紧性的假设下，得到了定义在Orlicz空间上的短缺风险测度的鲁棒表示结果.我们还讨论了一个具有序列紧性的例子的构造。
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.