Convex ordering for random vectors using predictable representation

TL;DR

This paper establishes convex ordering results for multi-dimensional random vectors with predictable representations involving Brownian motion and jumps, using advanced stochastic calculus techniques.

Contribution

It extends convex ordering results from one-dimensional to multi-dimensional vectors and introduces a geometric interpretation related to jump characteristics.

Findings

Convex ordering holds for vectors with predictable representations involving jumps.

A geometric interpretation links convex ordering to jump heights and intensities.

The method employs forward-backward stochastic calculus for the analysis.

Abstract

We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends previous results in the one-dimensional case. We also study a geometric interpretation of convex ordering for discrete measures in connection with the conditions set on the jump heights and intensities of the considered processes.