Reference : An ordinal approach to risk measurement
Scientific congresses, symposiums and conference proceedings : Paper published in a book
Physical, chemical, mathematical & earth Sciences : Mathematics
An ordinal approach to risk measurement
Cardin, Marta []
Couceiro, Miguel mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Mathematical and Statistical Methods for Actuarial Sciences and Finance
Springer -Verlang
Mathematical and Statistical Methods for Actuarial Sciences and Finance
[en] Completely distributive lattice ; invariance ; continuity ; Sugeno integra ; risk measure ; quantile
[en] In this short note, we aim at a qualitative framework for modeling multivariate risk. To this extent, we consider completely distributive lattices as underlying universes, and make use of lattice functions to formalize the notion of risk measure. Several properties of risk measures are translated into this general setting, and used to provide axiomatic characterizations. Moreover, a notion of quantile of a lattice-valued random variable is proposed, which is shown to retain several desirable properties of its real-valued counterpart.

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