The Conditional Convex Order and a Comparison Inequality

Christofides, Tasos C and Hadjikriakou, Milto (2015) The Conditional Convex Order and a Comparison Inequality. Stochastic Analysis and Applications, 33 (2). pp. 259-270. ISSN 0736-2994

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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 F-associated random variables with that of F-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).

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