Upper Comonotonicity and Risk Aggregation Under Dependence Uncertainty
研究了依赖不确定性对尾部风险度量的影响，提出正则依赖度量概念，发现微小正相关可导致尾部完全相关而之前看似独立，并证明在任意小正相关下聚合损失的尾部风险可能与完全相关时相同。
ABSTRACT In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multimarginal couplings, as a generalization of well‐known correlation statistics such as the Pearson correlation. The first main result states that even an arbitrarily small positive dependence between losses can result in perfectly correlated tails beyond a certain threshold and seemingly complete independence before this threshold. In a second step, we focus on the aggregation of individual risks with known marginal distributions by means of arbitrary nondecreasing left‐continuous aggregation functions. In this context, we show that under an arbitrarily small positive dependence, the tail risk of the aggregate loss might coincide with the one of perfectly correlated losses. A similar result is derived for expectiles under mild conditions. In a last step, we discuss our results in the context of credit risk, analyzing the potential effects on the value at risk for weighted sums of Bernoulli distributed losses.