Help proving change of measure formula in Piterbarg book

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Help proving change of measure formula in Piterbarg book

Postby selftaught » Mon Dec 09, 2013 2:56 am

Hello all,

In the chapter 1 of Piterbarg's book in the Radon-Nykodym derivative section, proving the below is referred to as a 'simple conditioning exercise', but I am having great difficulties:

EtQ [Y(T)] = EtP [R Y(T)] / EtP [R]

where :
R = dQ/dP = Radon-Nykodym derivative
P and Q are measures
EtP / EtQ is the conditional expectation wrt given a fitration Ft and measure P/Q
0 <t < T
Y(T) is FT measurable

please can someone suggest some clues ?

In general, to prove the a.s. equality fof 2 random variables X and Y, do I always start from first principles ?
ie prove that for any set A, E (1A X) = E (1A Y) with 1A indicator function of set A

Piterbarg's book is in Prof. Joshi's mandatory reading list which is why I am asking here

Many thanks
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