Multivariate convex orderings, dependence, and stochastic equality

Marco Scarsini (1, 2)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 Dipartimento di Scienze Economiche e Aziendali

We consider the convex ordering for random vectors and some weaker versions of it, like the convex ordering for linear combinations of random variables. First we establish conditions of stochastic equality for random vectors that are ordered by one of the convex orderings. Then we establish necessary and sufficient conditions for the convex ordering to hold in the case of multivariate normal distributions and sufficient conditions for the positive linear convex ordering (without the restriction to multi-normality).

Keywords: Dilation; copula; linear convex ordering; stochastic dominance; multivariate normal distribution

Domains: Economy and decision science

Marco Scarsini. Multivariate convex orderings, dependence, and stochastic equality. Journal of Applied Probability, 1998, Vol. 35, N°1, pp. 93-103. ⟨hal-00541775⟩