Article ID Journal Published Year Pages File Type
5076911 Insurance: Mathematics and Economics 2012 8 Pages PDF
Abstract

In actuarial theory, the Lp-metric is used to evaluate how well a probability distribution approximates another one. In the context of the distorted expectation hypothesis, the actuary replaces the original probability distribution by a distorted probability, so it makes sense to interpret the Lp-metric between them as a characteristic of the underlying random variable. We show in this paper that this is a characteristic of the variability of the random variable, study its properties and give some applications.

► We interpreted the Lp-metric between a probability distribution and its distortion as a measure of dispersion. ► We show that the measure satisfies the axioms of Bickel and Lehmann (1976). ► In particular, this measure is consistent with the dispersive order. ► We suggest a family of premium principles based on the new family of measures of dispersion.

Related Topics
Physical Sciences and Engineering Mathematics Statistics and Probability
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