  In this paper we introduce a sublinear conditional expectation with respect
to a family of possibly nondominated probability measures on a progressively
enlarged filtration. In this way, 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.
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.
