Esscher principle

The Esscher principle is a insurance premium principle. It is given by $pi\; [X]\; =E\; [Xe^\{hX\}]\; /E\; [e^\{hX\}]$, 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.