= Nonnegative state prices need not exclude arbitrage
{title2=$p\ge0\text{ is weaker than }p>0$}
If a traded payoff matrix $A$ has initial price vector $q=A^Tp$ with $p\ge0$, there cannot be a negative-cost <portfolio> with nonnegative terminal payoff. Nevertheless a nonzero nonnegative attainable payoff supported only in zero-price states can cost zero and give an <arbitrage>. When every state has positive physical <probability>, excluding this possibility requires strictly positive <Arrow state prices>, not merely a nonnegative supporting vector.
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