We consider two financial markets each of which has no arbitrage. We assume that no one trades in both markets, and that any claim traded in both markets trades at the same price. If someone could trade in both markets, he could construct new claims consisting of sums of claims in the two markets at prices equal to the sum of their market prices. Under what conditions will this new trader be unable to construct an arbitrage? We provide additional conditions under which this holds, and two interesting examples.

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