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. Furthermore, we study the superhedging approach in continuous time for payment streams under model uncertainty, and establish several equivalent versions of dynamic robust superhedging duality. These results close the gap between robust framework for financial market, which is recently studied in an intensive way, and the one for credit and insurance markets, which is limited in the present literature only to some very specific cases.
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