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Abstract We develop a convex‐optimization clustering algorithm for heterogeneous financial networks, in the presence of arbitrary or even adversarial outliers. In the stochastic block model with heterogeneity parameters, we penalize nodes whose degree exhibit unusual behavior beyond inlier heterogeneity. We prove that under mild conditions, this method achieves exact recovery of the underlying clusters. In absence of any assumption on outliers, they are shown not to hinder the clustering of the inliers. We test the performance of the algorithm on semi‐synthetic heterogenous networks reconstructed to match aggregate data on the Korean financial sector. Our method allows for recovery of sub‐sectors with significantly lower error rates compared to existing algorithms. For overlapping portfolio networks, we uncover a clustering structure supporting diversification effects in investment management. 

We introduce threshold growth in the classical threshold contagion model, or equivalently a network of Cramér-Lundberg processes in which nodes have downward jumps when there is a failure of a neighboring node. Choosing the configuration model as underlying graph, we prove fluid limits for the baseline model, as well as extensions to the directed case, state-dependent interarrival times and the case of growth driven by upward jumps. We obtain explicit ruin probabilities for the nodes according to their characteristics: initial threshold and in- (and out-) degree. We then allow nodes to choose their connectivity by trading off link benefits and contagion risk. We define a rational equilibrium concept in which nodes choose their connectivity according to an expected failure probability of any given link and then impose condition that the expected failure probability coincides with the actual failure probability under the optimal connectivity. We show existence of an asymptotic equilibrium and convergence of the sequence of equilibria on the finite networks. In particular, our results show that systems with higher overall growth may have higher failure probability in equilibrium. 

We develop a model for contagion in reinsurance networks by which primary insurers’ losses are spread through the network. Our model handles general reinsurance contracts, such as typical excess of loss contracts. We show that simpler models existing in the literature—namely proportional reinsurance—greatly underestimate contagion risk. We characterize the fixed points of our model and develop efficient algorithms to compute contagion with guarantees on convergence and speed under conditions on network structure. We characterize exotic cases of problematic graph structure and nonlinearities, which cause network effects to dominate the overall payments in the system. Last, we apply our model to data on real-world reinsurance networks. Our simulations demonstrate the following. (1) Reinsurance networks face extreme sensitivity to parameters. A firm can be wildly uncertain about its losses even under small network uncertainty. (2) Our sensitivity results reveal a new incentive for firms to cooperate to prevent fraud, because even small cases of fraud can have outsized effect on the losses across the network. (3) Nonlinearities from excess of loss contracts obfuscate risks and can cause excess costs in a real-world system. This paper was accepted by Baris Ata, stochastic models and simulation.