The Esscher principle is an insurance premium principle. It is given by

\pi,h E e^E^/math>, where h is a strictly positive parameter. This premium is the net premium for a risk Y=Xe^/m_X(h), where m_X(h) denotes the

moment generating function In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compar ...

. The Esscher principle is a

risk measure In financial mathematics, a risk measure is used to determine the amount of an asset or set of assets (traditionally currency) to be kept in reserve. The purpose of this reserve is to make the risks taken by financial institutions, such as ban ...

used in actuarial sciences that derives from the

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 . Def ...

. This risk measure does not respect the positive homogeneity property of

coherent risk measure In the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent risk ...

for

h>0

References

{{bank-stub Actuarial science