I'm struggling with an application of bayes rule in a proof and I hope you can help me.
At first some preliminaries:
**P(t,T) is the price of a Zero-Coupon-Bond and B(t) is a discount factor<<--I think this isnt necessary to know in order to understand the problem below. But just for the completeness.
We have a prop measure Q and define an equivalent prop. measure by
on a Filtration F_T, generated by Brownian Motions.
In my context we have in particulary for
Now one can show, that is a martingale.
But I do not understand the key step in the argumentation where bayes rule is used. The argumentation is for
The first equation is justified by bayes rule. But how?
I think it should be something like:
Represent the left Expectation through the Radon-Nikodym-Derivative and then use bayes, but I just can't complete it.
P.s. If some more "context" is needed, just say. But, I think the problem above is just a pure stochastic question.