A note on gg-expectation with comonotonic additivity

This paper proves that if an g  -expectation Eg[·]Eg[·] satisfies comonotonic additivity, then the corresponding generator g must be independent of y and be positively homogeneous with respect to z  ; furthermore, if Eg[·]Eg[·] is also subadditive, then the conditional g-expectation will also satisfy comonotonic additivity.