论文标题
带有给定风险因素边际分布的风险的最大光谱度量
Maximum Spectral Measures of Risk with given Risk Factor Marginal Distributions
论文作者
论文摘要
我们考虑确定损失光谱风险度量值的上限的问题，这是两个因素的一般非线性函数，其边际分布是已知的，但其联合分布尚不清楚。这些因素可能会在完全可分开的度量空间中取值。我们介绍了最大光谱度量（MSP）的概念，这是对因素之间的依赖性损失的最坏情况频谱风险度量。 MSP承认公式作为解决优化问题的解决方案，该解决方案与最佳传输问题相同，但具有更一般的目标函数。我们提出的结果类似于Kantorovich二元性，并研究了最佳值函数的连续性和最佳解决方案相对于边缘分布的扰动。此外，我们提供了一个渐近结果，该结果表征了从有限样品空间模拟因子分布时最佳值函数的限制分布。还检查了预期不足和最大预期缺口的特殊情况。
We consider the problem of determining an upper bound for the value of a spectral risk measure of a loss that is a general nonlinear function of two factors whose marginal distributions are known, but whose joint distribution is unknown. The factors may take values in complete separable metric spaces. We introduce the notion of Maximum Spectral Measure (MSP), as a worst-case spectral risk measure of the loss with respect to the dependence between the factors. The MSP admits a formulation as a solution to an optimization problem that has the same constraint set as the optimal transport problem, but with a more general objective function. We present results analogous to the Kantorovich duality, and we investigate the continuity properties of the optimal value function and optimal solution set with respect to perturbation of the marginal distributions. Additionally, we provide an asymptotic result characterizing the limiting distribution of the optimal value function when the factor distributions are simulated from finite sample spaces. The special case of Expected Shortfall and the resulting Maximum Expected Shortfall is also examined.
