Orlicz空间的可分性与稳健性：金融与经济观点
Separability vs. robustness of Orlicz spaces: financial and economic perspectives
摘要：
本文研究了鲁棒Orlicz空间作为鲁棒$L^p$ -空间的推广.这种空间的两种构造是不同的，自上而下的方法和自下而上的方法。我们证明了鲁棒Orlicz空间或其子空间的可分性在先验集的支配性和缺乏序完备性方面具有非常强的意义。我们的研究结果对稳健金融领域有着微妙的影响。例如，有界连续函数关于最坏情况的$L^p$ -范数的范数闭包，如在$G$ -框架中所考虑的，导致与经典$L^1$ -空间的子格同构的空间，然而，缺乏任何形式的序完备性。我们进一步证明了在非支配不确定性下期权的拓扑支撑力总是有限的。
英文摘要：
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.
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