In this paper we provide a new criterion for the comparison of claims, when we have conditional claims arising in stop loss contracts or contracts with franchise deductible. These stochastic comparisons are made on the basis of the Tail Value at Risk (also known as conditional tail expectation), just for a fixed level and beyond. In particular, we explain the interest of comparing these quantities, study some preservation properties and, in addition, we provide sufficient conditions for its study. Finally we illustrate its usefulness with some examples.

翻译：本文提出了一种新的索赔比较准则，适用于止损合同或免赔额合同中出现的条件索赔情形。这些随机比较建立在尾部风险价值（亦称条件尾部期望）的基础上，仅针对固定水平及其以上范围进行。我们特别阐释了比较这些量的意义，研究了若干保持性质，并提供了研究所需的充分条件。最后通过若干实例说明了该方法的实用性。