The Conditional Convex Order and a Comparison Inequality

Abstract

In this article, we define the conditional convex order, that is, a stochastic ordering between random variables given a sub-σ-algebra F. For the conditional convex order, we present a few representative results. In addition, we prove a comparison inequality, which, in a special case orders conditionally the partial sum of -associated random variables with that of -independent random variables. This latter result extends one of the main theorems of Boutsikas and Vaggelatou (“On the distance between convex-ordered random variables, with applications. Adv. in Appl. Probab., 34(2002):349–374).

Keywords:

• ℱ-independent random variables
• ℱ-associated random variables
• Conditionally negatively associated random variables
• Conditional N-demimartingales
• Convex order
• Conditional demimartingales

Mathematics Subject Classification:

• 60E15
• 60G48