A dynamic contagion risk model with recovery features
| Autor: | Agnès Sulem, Hamed Amini, Andreea Minca |
|---|---|
| Přispěvatelé: | Georgia State University, University System of Georgia (USG), Cornell University [New York], Mathematical Risk Handling (MATHRISK), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Random graph
Sequence Mathematical optimization Degree (graph theory) Financial stability General Mathematics insurance-reinsurance networks default contagion Management Science and Operations Research Computer Science Applications [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Interbank network Collective risk theory Convergence (routing) systemic risk Systemic risk Graph (abstract data type) Node (circuits) random graphs Mathematics |
| Zdroj: | Mathematics of Operations Research Mathematics of Operations Research, 2021, ⟨10.1287/moor.2021.1174⟩ Mathematics of Operations Research, INFORMS, 2021, ⟨10.1287/moor.2021.1174⟩ |
| ISSN: | 0364-765X 1526-5471 |
| DOI: | 10.1287/moor.2021.1174⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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