论文标题
有限产品空间中的Choquet风险度量的界限含糊不清
Bounds on Choquet Risk Measures in Finite Product Spaces with Ambiguous Marginals
论文作者
论文摘要
我们研究了发现两个风险因素的非线性功能的上限和下限的问题，当风险因素的边际分布模棱两可并以边缘空间的非累加措施表示，并且产品空间上的关节非addive分布是未知的。我们将这个问题视为将最佳运输问题概括为非辅助措施设置的概括。我们为有限边缘空间提供了最佳解决方案的明确特征，并研究了它们的一些特性。我们进一步讨论了与线性编程的连接，表明能力的最佳传输问题是线性程序，我们还明确地表征了它们的双重性能。最后，我们研究了一系列数值示例，包括与经典最佳运输问题的比较以及对应交易方面的信用风险的应用。
We investigate the problem of finding upper and lower bounds for a Choquet risk measure of a nonlinear function of two risk factors, when the marginal distributions of the risk factors are ambiguous and represented by nonadditive measures on the marginal spaces and the joint nonadditive distribution on the product space is unknown. We treat this problem as a generalization of the optimal transport problem to the setting of nonadditive measures. We provide explicit characterizations of the optimal solutions for finite marginal spaces, and we investigate some of their properties. We further discuss the connections with linear programming, showing that the optimal transport problems for capacities are linear programs, and we also characterize their duals explicitly. Finally, we investigate a series of numerical examples, including a comparison with the classical optimal transport problem, and applications to counterparty credit risk.
