文章基本信息

标题：Robustness regions for measures of risk aggregation
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作者：Silvana M. Pesenti ; Pietro Millossovich ; Andreas Tsanakas 等
期刊名称：Dependence Modeling
电子版ISSN：2300-2298
出版年度：2016
卷号：4
期号：1
页码：348-367
DOI：10.1515/demo-2016-0020
出版社：Walter de Gruyter GmbH
摘要：One of risk measures’ key purposes is to consistently rank and distinguish between different risk profiles.From a practical perspective, a risk measure should also be robust, that is, insensitive to small perturbations in input assumptions.It is known in the literature [14, 39], that strong assumptions on the risk measure’s ability to distinguish between risks may lead to a lack of robustness.We address the trade-off between robustness and consistent risk ranking by specifying the regions in the space of distribution functions, where law-invariant convex risk measures are indeed robust.Examples include the set of random variables with bounded second moment and those that are less volatile (in convex order) than random variables in a given uniformly integrable set.Typically, a risk measure is evaluated on the output of an aggregation function defined on a set of random input vectors.Extending the definition of robustness to this setting, we find that law-invariant convex risk measures are robust for any aggregation function that satisfies a linear growth condition in the tail, provided that the set of possible marginals is uniformly integrable.Thus, we obtain that all law-invariant convex risk measures possess the aggregation-robustness property introduced by [26] and further studied by [40].This is in contrast to the widely-used, non-convex, risk measure Value-at-Risk, whose robustness in a risk aggregation context requires restricting the possible dependence structures of the input vectors.
关键词：Convex risk measures ; Aggregation ; Value-at-Risk ; Robustness ; Continuity