A dynamic contagion risk model with recovery features
Amini, Hamed; Chen, Rui; Minca, Andreea; Sulem, Agnès (2019), A dynamic contagion risk model with recovery features. https://basepub.dauphine.fr/handle/123456789/20685
TypeDocument de travail / Working paper
External document linkhttps://hal.inria.fr/hal-02421342
Cahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
Swiss Finance Institute [Lausanne]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Computer Systems Lab - School of Electrical and Computer Engineering - Cornell University [CSL]
Abstract (EN)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 inter-arrival 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 as well as 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.
Subjects / KeywordsRandom graphs; Collective risk theory; Systemic risk; Default contagion; Interbank network; Insurance-reinsurance networks; Financial stability
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