= Negative minimal density in an arbitrage-free one-period market
Let a discounted gain $Y$ take values $-1,1,10$ with physical probabilities $1/10,4/5,1/10$. Then $m=17/10$ and $C=801/100$, so the <minimal martingale measure in a one-period market> has signed density $Z_*(10)=-610/801$. Nevertheless $(109/200,89/200,1/100)$ is a strictly positive pricing probability with zero mean gain. Thus absence of <arbitrage> does not ensure positivity of the minimal density. The minimum-norm identity holds for signed pricing densities; interpretation as a <dominated martingale measure> requires nonnegativity.
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