  We consider a banking network represented by a system of stochastic
differential equations coupled by their drift. We assume a core-periphery
structure, and that the banks in the core hold a bubbly asset. The banks in the
periphery have not direct access to the bubble, but can take initially
advantage from its increase by investing on the banks in the core. Investments
are modeled by the weight of the links, which is a function of the robustness
of the banks. In this way, a preferential attachment mechanism towards the core
takes place during the growth of the bubble. We then investigate how the bubble
distort the shape of the network, both for finite and infinitely large systems,
assuming a non vanishing impact of the core on the periphery. Due to the
influence of the bubble, the banks are no longer independent, and the law of
large numbers cannot be directly applied at the limit. This results in a term
in the drift of the diffusions which does not average out, and that increases
systemic risk at the moment of the burst. We test this feature of the model by
numerical simulations.
