We study a deﬁnition of subjective beliefs applicable to preferences that allow for the perception of ambiguity, and provide a characterization of such beliefs in terms of market behavior. Using this deﬁnition, we derive necessary and sufﬁcient conditions for the efﬁciency of ex ante trade and show that these conditions follow from the fundamental welfare theorems. When aggregate uncertainty is absent, our results show that full insurance is efﬁcient if and only if agents share some common subjective beliefs. Our results hold for a general class of convex preferences, which contains many functional forms used in applications involving ambiguity and ambiguity aversion. We show how our results can be articulated in the language of these functional forms, conﬁrming results existing in the literature, generating new results, and providing a useful tool for applications.