A class of bivariate stochastic orderings, with applications in actuarial sciences

Abstract

This paper is concerned with the bivariate extension of a wide class of univariate orderings said to be of convex-type. Attention is paid to random vectors valued in a rectangle or an orthant of the real plane. Various orderings used in probability and statistics (such as the stochastic dominance, the upper orthant order, the orthant convex order, the correlation order and the supermodular order) can be seen as particular cases. The practical applications of these orderings seem to be very promising, especially in actuarial sciences.