Esscher principle

The Esscher principle is an insurance premium principle. It is given by π [ X , h ] = E [ X e h X ] / E [ e h X ] , where h is a strictly positive parameter. This premium is the net premium for a risk Y = X e h X / 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 the Esscher transform. This risk measure does not respect the positive homogeneity property of coherent risk measure for h > 0 .