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A dynamic contagion risk model with recovery features

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A_dynamic_contagion_risk_model_with_recovery_features.pdf (569.5Kb)
Date
2019
Publisher city
Paris
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Publishing date
12-2019
Link to item file
https://hal.inria.fr/hal-02421342
Dewey
Probabilités et mathématiques appliquées
Sujet
Random graphs; Collective risk theory; Systemic risk; Default contagion; Interbank network; Insurance-reinsurance networks; Financial stability
URI
https://basepub.dauphine.fr/handle/123456789/20685
Collections
  • CEREMADE : Publications
Metadata
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Author
Amini, Hamed
455165 Swiss Finance Institute [Lausanne]
Chen, Rui
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Minca, Andreea
72421 Computer Systems Lab - School of Electrical and Computer Engineering - Cornell University [CSL]
Sulem, Agnès
34587 INRIA Rocquencourt
Type
Document de travail / Working paper
Item number of pages
36
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.

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