Lida pointed out CoM (change of measure) means that given a pdf bell curve, we change its mean while preserving its “shape”! I guess the shape is the LN shape?
I guess CoM doesn’t always preserve the shape.
Lida explained how to change one Expectation integral into another… Radon Nikodym.
The concept of operating under a measure (call it f) is fundamental and frequently mentioned but abstract…
Aha – Integrating the expectation against pdf f() is same as getting the expectation under measure-f. This is one simple, if not rigorous, interpretation of operating under a given measure. I believe there’s no BM or GBM, or any stochastic process at this stage — she was describing how to transform one static pdf curve to another by changing measure. I think Girsanov is different. It’s about a (stochastic) process, not a static distribution.