We characterize the evolution over time of a network of credit relations among financial agents as a system of coupled stochastic processes.Each process describes the dynamics of individual financial robustness, while the coupling results from a network of liabilities among agents.The average level of risk diversification of the agents coincides with the density of links in the network.In addition to a process of diffusion of financial distress, we also consider a discrete process of default cascade, due to the re-evaluation of agents' assets.In this framework we investigate the probability of individual defaults as well as the probability of systemic default as a function of the network density.While it is usually thought that diversification of risk always leads to a more stable financial system, in our model a tension emerges between individual risk and systemic risk.As the number of counterparties in the credit network increases beyond a certain value, the default probability, both individual and systemic, starts to increase.This tension originates from the fact that agents are subject to a financial accelerator mechanism.In other words, individual financial fragility feeding back on itself may amplify the effect of an initial shock and lead to a full fledged systemic crisis.The results offer a simple possible explanation for the endogenous emergence of systemic risk in a credit network.
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