Esscher principle

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The Esscher principle is a insurance premium principle. It is given by \pi[X,h]=E[Xe^{hX}]/E[e^{hX}], where h is a strictly positive parameter. This premium is in fact the net premium for a risk Y=Xe^{hX}/m_X(h), where m_X(h) denotes the moment generating function.

The Esscher principle is a Risk measure used in actuarial sciences that derives from Esscher transform. This risk measure doesn't respect the positive homogeneity propertie of Coherent risk measure for h>0.