论文标题
可分离性与Orlicz空间的鲁棒性：财务和经济观点
Separability vs. robustness of Orlicz spaces: financial and economic perspectives
论文作者
论文摘要
我们研究了强大的Orlicz空间，作为强大的$ l^p $空间的概括。区分了此类空间的两个结构，一种自上而下的方法和一种自下而上的方法。我们表明，稳健的Orlicz空间或它们的子空间的可分离性在一组先验和缺乏秩序完整性方面具有很大的影响。我们的结果对健壮的财务领域具有微妙的影响。例如，在$ g $ framework中考虑的最坏情况下，有限连续函数的规范关闭，导致空间导致晶格同构的空间，以使经典$ l^1 $ - 空间缺乏均等的sublattice，但是，缺乏任何形式的订单完整性。我们进一步表明，在非主导的不确定性下，期权的拓扑跨度始终受到限制。
We investigate robust Orlicz spaces as a generalisation of robust $L^p$-spaces. Two constructions of such spaces are distinguished, a top-down approach and a bottom-up approach. We show that separability of robust Orlicz spaces or their subspaces has very strong implications in terms of the dominatedness of the set of priors and the lack of order completeness. Our results have subtle implications for the field of robust finance. For instance, norm closures of bounded continuous functions with respect to the worst-case $L^p$-norm, as considered in the $G$-framework, lead to spaces which are lattice isomorphic to a sublattice of a classical $L^1$-space lacking, however, any form of order completeness. We further show that the topological spanning power of options is always limited under nondominated uncertainty.
