A Dynamic Contagion Risk Model With Recovery Features

49 Pages Posted: 13 Aug 2019 Last revised: 4 Aug 2020

See all articles by Hamed Amini

Hamed Amini

Georgia State University

Andreea Minca

Cornell University

Agnes Sulem

French National Institute for Research in Computer Science and Control (INRIA)

Date Written: August 9, 2019

Abstract

We introduce threshold growth in the classical threshold contagion model, or equivalently a network of Cramer-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.

Keywords: collective risk theory, systemic risk, default contagion

JEL Classification: G01, G18

Suggested Citation

Amini, Hamed and Minca, Andreea and Sulem, Agnes, A Dynamic Contagion Risk Model With Recovery Features (August 9, 2019). Available at SSRN: https://ssrn.com/abstract=3435257 or http://dx.doi.org/10.2139/ssrn.3435257

Hamed Amini (Contact Author)

Georgia State University ( email )

Georgia State University
Atlanta, GA 30303
United States

Andreea Minca

Cornell University ( email )

222 Rhodes Hall
Ithaca, NY NY 14853
United States

HOME PAGE: http://people.orie.cornell.edu/acm299/

Agnes Sulem

French National Institute for Research in Computer Science and Control (INRIA) ( email )

40 avenue Halley
Villeneuve, 59650
France

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