A Dynamic Contagion Risk Model with Recovery Features

Hamed Amini (), Andreea Minca () and Agnès Sulem ()
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Hamed Amini: Department of Risk Management and Insurance, Georgia State University, Atlanta, Georgia 30303
Andreea Minca: School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14850
Agnès Sulem: Institut National de Recherche en Sciences et Technologies du Numérique Paris, 75589 Paris Cedex 12, France

Mathematics of Operations Research, 2022, vol. 47, issue 2, 1412-1442

Abstract: 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.

Keywords: 91B30; 91G50; 90B15; 90B50; 90B10; 91B15; 60J10; collective risk theory; systemic risk; default contagion; random graphs; interbank network; insurance-reinsurance networks; financial stability (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:2:p:1412-1442

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