损害多元化如何降低系统性风险
How Damage Diversification Can Reduce Systemic Risk
摘要：
我们考虑复杂网络中的风险分散问题。节点表示例如金融参与者，而加权链接表示例如金融义务（信贷/债务）。每个节点都有失败的风险，因为违约邻居造成的损失，这可能会导致大的故障级联。经典的风险分散策略通常忽略网络效应，因此建议如果可能的损失（即，暴露）在许多邻居之间（暴露多样化，ED）。但从复杂网络的角度来看，多样化意味着整个系统的连通性更高，这也可能导致节点故障风险增加。为了解决这个问题，我们提出了一个不同的策略（损害多样化，DD），即分散的损失，施加在相邻节点上，而不是节点本身发生的损失。在这里，我们量化的潜力DD相比，ED降低系统性风险。为此，我们开发了一个分支过程近似，我们推广到加权网络（几乎）任意的程度和权重分布。这使我们能够识别网络中的系统相关节点，即使它们的有向权重相差很大。在宏观层面上，我们提供了一个分析表达式的平均级联大小，量化系统性风险。此外，在中观层面上，我们根据节点的系统相关性计算节点的故障概率。
英文摘要：
We consider the problem of risk diversification in complex networks. Nodes represent e.g. financial actors, whereas weighted links represent e.g. financial obligations (credits/debts). Each node has a risk to fail because of losses resulting from defaulting neighbors, which may lead to large failure cascades. Classical risk diversification strategies usually neglect network effects and therefore suggest that risk can be reduced if possible losses (i.e., exposures) are split among many neighbors (exposure diversification, ED). But from a complex networks perspective diversification implies higher connectivity of the system as a whole which can also lead to increasing failure risk of a node. To cope with this, we propose a different strategy (damage diversification, DD), i.e. the diversification of losses that are imposed on neighboring nodes as opposed to losses incurred by the node itself. Here, we quantify the potential of DD to reduce systemic risk in comparison to ED. For this, we develop a branching process approximation that we generalize to weighted networks with (almost) arbitrary degree and weight distributions. This allows us to identify systemically relevant nodes in a network even if their directed weights differ strongly. On the macro level, we provide an analytical expression for the average cascade size, to quantify systemic risk. Furthermore, on the meso level we calculate failure probabilities of nodes conditional on their system relevance.
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