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Coherence and avoidance of sure loss for standardized functions and semicopulasErich Peter Klement,
Damjana Kokol-Bukovšek,
Blaž Mojškerc,
Matjaž Omladič,
Susanne Saminger,
Nik Stopar, 2024, original scientific article
Abstract: We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, $1$-increasing functions with value $1$ at $(1, 1, \ldots , 1)$. We characterize the existence of a $k$-increasing $n$-variate function $C$ fulfilling $A \le C \le B$ for standardized $n$-variate functions $A$, $B$ and discuss methods for constructing such functions. Our proofs also include procedures for extending functions on some countably infinite mesh to functions on the unit box. We provide a characterization when $A$ respectively $B$ coincides with the pointwise infimum respectively supremum of the set of all $k$-increasing $n$-variate functions $C$ fulfilling $A \le C \le B$.
Keywords: copulas, quasi-copulas, semicopulas, standardized function, coherence, avoidance of sure loss, k-increasing function
Published in DiRROS: 13.03.2024; Views: 116; Downloads: 61
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