英文标题：
《Robust risk aggregation with neural networks》
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作者：
Stephan Eckstein, Michael Kupper, Mathias Pohl
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最新提交年份：
2020
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英文摘要：
  We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure in a transportation distance (e.g. the Wasserstein distance), and additionally have the correct marginal structure. The goal is to find upper and lower bounds for integrals of interest with respect to distributions in this set. The described problem appears naturally in the context of risk aggregation. When aggregating different risks, the marginal distributions of these risks are known and the task is to quantify their joint effect on a given system. This is typically done by applying a meaningful risk measure to the sum of the individual risks. For this purpose, the stochastic interdependencies between the risks need to be specified. In practice the models of this dependence structure are however subject to relatively high model ambiguity. The contribution of this paper is twofold: Firstly, we derive a dual representation of the considered problem and prove that strong duality holds. Secondly, we propose a generally applicable and computationally feasible method, which relies on neural networks, in order to numerically solve the derived dual problem. The latter method is tested on a number of toy examples, before it is finally applied to perform robust risk aggregation in a real world instance.
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中文摘要：
我们考虑多元随机变量的分布部分不明确的情况。我们假设模糊性取决于依赖结构的水平，并且边际分布是已知的。此外，还提供了当前分布的最佳猜测，称为参考度量。我们使用的分布集在运输距离（如Wasserstein距离）上既接近给定的参考度量，又具有正确的边际结构。目标是找到关于该集中分布的感兴趣积分的上界和下界。所描述的问题自然出现在风险聚合的背景下。当聚合不同的风险时，这些风险的边际分布是已知的，任务是量化它们对给定系统的联合影响。这通常是通过对单个风险的总和应用有意义的风险度量来实现的。为此，需要指定风险之间的随机相关性。然而，在实践中，这种依赖结构的模型受到相对较高的模型模糊性的影响。本文的贡献有两点：首先，我们推导了所考虑问题的对偶表示，并证明了强对偶成立。其次，我们提出了一种普遍适用且计算可行的方法，该方法依赖于神经网络，以数值求解导出的对偶问题。后一种方法在许多玩具示例上进行了测试，然后才最终应用于在真实世界实例中执行稳健的风险聚合。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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