Before revision: In this paper we  extend the classic reduced-form setting for credit and insurance markets to the case under model uncertainty, when we consider a family of priors possibly mutually singular to each other . To this end, we introduce on a progressively enlarged filtration a sublinear conditional expectation with respect to a family of possibly nondominated probability measures .
After revision: In this paper we extend the classic reduced-form setting for credit and insurance markets to the case under model uncertainty, when we consider a family of priors possibly mutually singular to each other .