Systemic risk in finance and elsewhere

Systemic risk is often the unintended consequence of the attempt by individuals to reduce risk. I will present three simple models that illustrate this point: The first is a model of leveraged value investing funds, where we show how the act of a bank calling in a loan can amplify price fluctuations and lead to crashes; more sophisticated policies, such as Basel II, often make the situation worse. The second model is for leverage dynamics under market impact, where we show how the commonly used practice of mark-to-market accounting leads to a critical phenomenon in which the market impact of buying and selling can cause bankruptcy; we suggest an alternative method of accounting that fixes this by provided the information needed to avoid the critical point. The final model treats a network of leveraged funds (such as banks) who are connected by holding common assets, and shows how this can be treated as a branching process. I will argue that systemic risk in finance is often driven by disruptions in market ecology, which are driven by deviations from market efficiency, and thus are not well addressed by traditional theories that assume such inefficiencies away.