Mathematics writing question

Consider the 1−period model from class, with N > 0, S0 > 0, and 0 < d < 1 + r < u. Show that this model does not admit arbitrage if there are no securities other than savings or stock. That is, show that there is no way to make a portfolio such that X0 = 0, X1 ≥ 0, and either X1(H) > 0 or X1(T) > 0.

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