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Which of the following necessarily imply a violation of the no-arbitrage principle? Assume T > 0 and epsilon > 0.

(a) A portfolio which has zero value today, always non-negative value at T, and positive value at T for some sample outcomes ω with P({ω}) > 0.

(b) A portfolio which has zero value today and expected positive value at T.

(c) A portfolio which has value −epsilon today and zero value at T.

(d) A portfolio which has value epsilon today and expected positive value at T.

(e) A portfolio which has zero value today and value epsilon at T.

(f) A portfolio which has zero value today and positive value at T for some sample outcomes with positive probability.

(g) A portfolio which has zero value today, always non-negative value at T, and positive value at T for some sample outcomes.

(h) A portfolio which has zero value today, always non-negative value at T, and expected positive value at T.

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