Coherence and avoidance of sure loss for standardized functions and semicopulas

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 $(1,1,\dots ,1)$. 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 the method for constructing this function. 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 $A\le C\le B$.

32 pages, 2 figures, Paper was revised, some additional explanations were provided, some additiaonal references were added

Cited by in corpus (1)

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