We study portfolio allocation and characterize contracts issued by firms in the international financial market when investors exhibit ambiguity aversion and perceive ambiguity in assets issued in foreign locations. Increases in the variance of their risky production process cause firms to issue assets with a higher variable payment (equity). Hikes in investors' perceived ambiguity have the opposite effect, and lead to less risk-sharing. Entrepreneurs from capital-scarce countries finance themselves relatively more through debt than equity. They are thus exposed to higher volatility per unit of consumption. The expected returns on capital invested in capital-scarce countries may also be lower. Such results do not hold in the absence of ambiguity, that is, when investors only perceive risk. New facts uncovered from cross-country firm-level data are consistent with our model. •Contract issuance with ambiguity averse international investors is studied.•Increases in project risk cause firms to issue more equity and less debt.•Increases in ambiguity cause firms to issue less equity and sometimes more debt.•Firms in capital-scarce countries issue relatively more debt than equity.•New facts uncovered from cross-country firm-level data are consistent with our model.