VosePrincipleEsscher | Vose Software


See also: VosePrincipleEV, VosePrincipleRA, VosePrincipleStdev, Premium calculations

VosePrincipleEsscher(frequency distribution, severity distribution, h)



Example model

This function calculates the insurance premium for given frequency and severity distributions using the Esscher principle.

For an insurance policy the premium charged must be at least greater than the expected payout E[X]. Otherwise, according to the law of large numbers, in the long run the insurer will be ruined. The question is then: how much more should the premium be over the expected value?

The Esscher method calculates the ratio of the expected values of XehX to ehX

Premium =                            h > 0

The principle gets its name from the Esscher transform which converts a density function from f(x) to a*f(x)*Exp[b*x] where a, b are constants.