Linearities, Non-Linearities and Phase Transitions in Loss Diffusion Processes in Financial Networks

Banks and financial institutions are linked by financial obligations that form complex networks. These networks serve risk sharing purposes and become channels of contagion in the event of liquidity and insolvency shocks. The consequent processes of loss diffusion are usually non-linear and, in some cases, exhibit phase transitions from situations in which there is no default contagion to systemic crisis that involve the entire network. In this paper, I discuss the results of recent numerical simulations of contagion processes in financial networks that present some unexpected linearities.