= Solution
Suppose a strictly positive pricing density exists. Its weighted payment for any fixed holdings is <integrable>, and
$$
x^\top A_0=\mathbb E[\nu\,x^\top A_1].
$$
If the terminal payment is nonnegative and strictly positive on an <event> of positive <probability>, positivity of $\nu$ makes this <expected value> strictly positive. It cannot therefore have nonpositive initial cost. Thus the first form of <arbitrage> is incompatible with a positive pricing density. The existence argument in part (b) proves that this form occurs whenever separation within the payment span obstructs a density.
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