He guys,

I want to prove that for a sequence $\displaystyle X_{1},X_{2},... $ of independent random variables which have a standard normal distribution, that $\displaystyle Y_{n}=Exp\left(\sum^{n}_{k=1}X_{k}-(1/2)n\right) $ is a martingale.

I have that $\displaystyle E(Y_{n+1}\right)\left|Y_{n}\right)=E(Exp\left(X_{n +1}-1/2)Exp\left(\sum^{n}_{k=1}X_{k}-(1/2)n\right\right)|Exp\left(\sum^{n}_{k=1}X_{k}-(1/2)n \right)\right). $

What can I do know?

gr,

sung