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Let P(S,t) denote the price of an American put option at time t, and let p(S,t) denote the price of a European put option at

Let P(S,t) denote the price of an American put option at time t, and let p(S,t) denote the price of a European put option at time t. For every t < T. Prove that (regardless of whether there is a dividend) p(S,t)< P(S,t).

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