Management of systemic risks and cascade failures in a networked society

The qualification of risks lies in their systemic nature. A risk to one subsystem may present an opportunity to another subsystem. A systemic risk is the possibility that an event will trigger a loss of confidence in a substantial portion of the system serious enough to have adverse consequences on system performance. A systemic risk therefore impacts the integrity of the whole system. In this chapter, we use networks to address risks. A network, which is a collection of nodes with links between them, can be a useful representation of a system. For instance, network analysis can explain certain systemic risks in financial systems by modeling interactions among financial institutions. A network approach is also useful in mitigating large blackouts caused by cascade failure. In this case, instead of looking at the details of particular blackouts, we investigate the cascade dynamics as a series of blackouts using risk propagation models. We use a general framework of diffusion or contagion models to describe risk propagation in networks and investigate how network topology impacts risk propagation patterns. At the macroscopic level, systemic risk is measured as the fraction of failed nodes. We divide our discussion into two classes of diffusion. First, we discuss so-called progressive diffusion processes. Many diffusion processes are progressive in the sense that once a node switches from one state to another, it remains in that state in all subsequent time steps. The second class is non-progressive diffusion where, as time progresses, nodes can switch back and forth from one state to the other, depending on the states of their neighbors. Networks increase interdependency,creating challenges formanaging risks. This is especially apparent in areas such as financial institutions and enterprise risk management, where the actions of a single actor in an interconnected network can impact all the other actors in the network. The network is only as strong as its weakest link, and trade-offs are most often connected to a function that models system performance management. In this context, there is a class of problems, ranging