Abstract
It is shown that a distribution-free implicit price loading method, which sets prices using a modified Hardy-Littlewood majorant of the stop-loss ordered maximal random variable by given range, mean and variance, induces distribution-free safe layer-additive distortion pricing. As a by-product, Karlsruhe pricing turns out to be a valid linear approximation to Hardy-Littlewood pricing in case the coefficient of variation is sufficiently high.
Keywords: Choquet pricing; Distorted probability; Distribution-free method; Safeness property; Stochastic orders; Mean-variance analysis; Extremal random variables; Hardy-Littlewood majorant; Insurance layers; Karlsruhe principle
Volume
Vol. 22, Issue 3
Page
277-285
Year
1998
Categories
Business Areas
Reinsurance
Excess (Non-Proportional);
Financial and Statistical Methods
Loss Distributions
Extreme Values
Actuarial Applications and Methodologies
Ratemaking
Large Loss and Extreme Event Loading
Financial and Statistical Methods
Loss Distributions
Severity
Financial and Statistical Methods
Risk Pricing and Risk Evaluation Models
Publications
Insurance: Mathematics & Economics
