Ordre stochastique et applications

Abstract

The purpose of this memory is to systematically present and process the stochastic orders used in actuarial science and to prove that the mathematical expectation of the absolute value of the difference between two random variables not necessarily independent, it is a measure of its variability in the sense of Bickel and Lehmann, if we add conditions to these variables (by the notion of copulas), we will obtain new properties on this measure. We have also defined sufficient conditions to compare two random pairs, and we have mentioned two applications, the first is about insurance policy deductibles and limits, and the second is about insurance premium principles.