Esscher transform

In actuarial science, the Esscher transform is a transform that takes a probability density "f"("x") and transforms it to a new probability density "f"("x"; "h") with a parameter "h". It was introduced by F. Esscher in 1932 .
Definition.
Let "f"("x") be a probability density. Its Esscher transform is defined as
More generally, if "μ" is a probability measure, the Esscher transform of "μ" is a new probability measure "Eh"("μ") which has density
with respect to "μ".