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Quasi-Arithmetic Type Mean Generated by the Generalized Choquet Integral

Sebastian Wójcik
2020 Symmetry  
It is known that the quasi-arithmetic means can be characterized in various ways, with an essential role of a symmetry property. In the expected utility theory, the quasi-arithmetic mean is called the certainty equivalent and it is applied, e.g., in a utility-based insurance contracts pricing. In this paper, we introduce and study the quasi-arithmetic type mean in a more general setting, namely with the expected value being replaced by the generalized Choquet integral. We show that a functional
more » ... w that a functional that is defined in this way is a mean. Furthermore, we characterize the equality, positive homogeneity, and translativity in this class of means.
doi:10.3390/sym12122104 fatcat:p3jvjcngindhtpbcfqmcz43dpe