Premium Calculation: Why Standard Deviation Should Be Replaced By Absolute Deviation

Average absolute (instead of quadratic) deviation from median (instead of expectation) is better suited to determine the safety loading for insurance premiums than standard deviation: The corresponding premium functionals behave additive under the practically relevant risk sharing schemes between first insurer and reinsurer. Keywords: Premium principles; distorted probabilities. average absolute deviation; comonotonic additivity; distorted probabilities.