Mean residual life processes and associated submartingales

Abstract

We use Madan-Yor's argument to construct associated submartingales to a class of two-parameter processes that are ordered by the increasing convex dominance. This class includes processes which have MTP${}_2$ integrated survival functions. We prove that the integrated survival function of an integrable two-parameter process is MTP${}_2$ if and only if it is TP${}_2$ in each pair of arguments when the remaining argument is fixed. This result can not be deduced from known results since there are several two-parameter processes whose integrated survival functions do not have interval support. The MTP${}_2$ property of certain MRL processes is useful to exhibit numerous other processes having the same property.

23 pages, 1 figure

References in corpus (2)

• The Skorokhod embedding problem and its offspring
• MRL order, log-concavity and an application to peacocks