= Dominated martingale measure
{title2=$Q\ll P,\quad\mathbb E_QY=0$}
For discounted one-period asset gains $Y$, a dominated martingale measure is a <probability measure> $Q$ <absolutely continuous with respect to> the physical <probability measure> $P$, under which the gains have zero <expectation>. Its <Radon-Nikodym derivative> $Z$ satisfies $Z\geq0$, $\mathbb E_PZ=1$ and $\mathbb E_P[ZY]=0$. An <equivalent martingale measure> additionally has $Z>0$ <almost surely>. Absolute continuity permits some positive-probability physical states to receive zero pricing probability; equivalence does not.
Back to article page