A Dynamic Contagion Risk Model with Recovery Features

We introduce threshold growth in the classical contagion model, or equivalently a network of Cramér-Lundberg processes which nodes have downward jumps when there is failure neighboring node. Choosing configuration model as underlying graph, we prove fluid limits for baseline well extensions to directed case, state-dependent interarrival times and case driven by upward jumps. obtain explicit ruin probabilities according their characteristics: initial in- (and out-) degree. then allow choose connectivity trading off link benefits risk. define rational equilibrium concept an expected probability any given impose condition that coincides with actual under optimal connectivity. show existence asymptotic convergence sequence equilibria on finite networks. In particular, our results systems higher overall may equilibrium.