A dynamic contagion risk model with recovery features - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematics of Operations Research Year : 2021

A dynamic contagion risk model with recovery features

Hamed Amini
  • Function : Author
  • PersonId : 1116734
Agnès Sulem
  • Function : Author
  • PersonId : 865285


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.
Fichier principal
Vignette du fichier
NetworksWithGrowthFeb15_R2_MOR.pdf (909.75 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-02421342 , version 1 (20-12-2019)
hal-02421342 , version 2 (21-01-2022)



Hamed Amini, Andreea Minca, Agnès Sulem. A dynamic contagion risk model with recovery features. Mathematics of Operations Research, 2021, ⟨10.1287/moor.2021.1174⟩. ⟨hal-02421342v2⟩
132 View
400 Download



Gmail Mastodon Facebook X LinkedIn More