Hello,
What is r ?
Hello all, I have a bit of a problem at the moment solving this task. I done half of it already, just can solve it for the other half. Hope u can help! Thanks =)
Let where all are independent with distribution, find a relation such that r can be expressed in terms of
Here's my working out so far:
Def of a martingale:
Hence:
Now because where
That becomes:
From that point im not too sure what to do. If anyone can help me or tell me what to do would be much appreciated. Thanks.
Yes, but you're not clear at all !!!!!
I'll assume you want to find r such that is a martingale. If that's not the case, then read again what you wrote...
Okay with this.
Now this can also be written :
Since the Yn are independent, we'll have a product of expectations :
Since Y1,...,Yn are Sn-measurable,
Since is independent with ,
So finally, you want r such that
which means to find r such that
Have a look at the MGF of a normal distribution when t=1 and you're done...
(to simplify a bit all these things, you could've written in terms of , but it doesn't really matter, it's just more beautiful)