Comonotone lower probabilities with robust marginal distributions functions

Abstract One of the usual dependence structures between random variables is comononicity, which refers to that increase or decrease simultaneously. Besides good mathematical properties, comonotonicity has been applied in choice theory under risk finance, among many other fields. The problem arises when marginal distribution functions are only partially known, hence we know bounds their values. This can be mathematically modelled using p-boxes, allowing us build a bridge with imprecise probabilities. paper investigates existence, construction and uniqueness joint (imprecise) comonotone model given p-boxes. In particular, not unique it exists, follow philosophy probability characterise conditions there exists least-committal model, called natural extension.