This paper solves the optimal portfolio choice problem in a multi-asset incomplete market model with ambiguous jump risks.We derive the optimal portfolio rules as well as the worst-case probability explicitly.Out of fear for extreme tail events in the worst case,an ambiguity-averse investor may hold only part or even none of the available risky assets.In a calibration exercise,we compare optimal portfolio outcomes between two models with jump sizes following a normal distribution and a tail distribution,respectively.In stark contrast to the negligible loss under rational expectation,sizable economic losses are incurred in the model with ambiguous tail risk when the investor ignores extreme tail events.