Do you have any intuition behind the following theorem :
A financial market is complete if and only iff there exists a unique equivalent martingale measure.
I understand the easier version of the theorem. Now I m trying to understand the dynamics of this theorem.
In particular, I can't understand why there must be only one unique. Can someone explain it to me ? I don't mind you take the simplest example, I just want to understand how the proof works in easy example.
The explaination that I have for now is that
$X_1$ is replicable, iff it has a unique AFP.
This is because here we can reproduce the pay off of $X_1$ by a combination of other strategies. Then, because the price of other instruments is fixed, the AFP must be unique.
Now having a unique AFP makes $ E^\mathbb Q [ X_1 ]$ constant accross all equivalent martingale measures. I don't understand this part . Is it simply because changing the measure doesn't change the outcome of a constant ?
What do you think of that?