Esscher transform


In actuarial science, the Esscher transform is a transform that takes a [probability Radon–Nikodym derivative|density function|probability density] f and transforms it to a new probability density f with a parameter h. It was introduced by F. Esscher in 1932.

Definition

Let f 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 which has density
with respect to μ.

Basic properties

; Combination
; Inverse
; Mean move