VosePrincipleEsscher

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VosePrincipleEsscher(frequency distribution, severity distribution, h)

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

Frequency distribution - a frequency distribution object.
Severity distribution - a severity distribution object.
h - see the formula below.

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 Xe^hX to e^hX

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.