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Risk Neutral Pricing and Financial Mathematics: A Primer by John L. Teall, Peter M. Knopf

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Here, we have defined the Radon–Nikodym derivative for our change of measure:

dd(x)=ξ(x)=eμx+μ22 (6.7)

image (6.7)

This change of measure allows us to take a random variable that had a nonzero mean with respect to one probability space and convert the probability space so that the random variable has a zero mean with respect to the new probability space, while leaving its variance unchanged. After illustrating and generalizing this change, we will perform a similar change of measure on a Brownian motion process.

Illustration: Change of Normal Density

Suppose that we were to begin with a random variable X with mean μ under probability measure , and ...

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