Title: The Theory of Systemic Risk
Description: Systemic risk is an issue of great concern in modern financial markets as well as, more broadly, in the management of complex business and engineering systems. It refers to the risk of collapse of an entire complex system, as a result of the actions taken by the individual component entities or agents that comprise the system. We investigate the topic of systemic risk from the perspectives of measurement, structural sources, and risk factors. In particular, we propose an axiomatic framework for the measurement and management of systemic risk based on the simultaneous analysis of outcomes across agents in the system and over scenarios of nature. Our framework defines a broad class of systemic risk measures that accommodate a rich set of regulatory preferences. This general class of systemic risk measures captures many specific measures of systemic risk that have recently been proposed as special cases, and highlights their implicit assumptions. Moreover, the systemic risk measures that satisfy our conditions yield decentralized decompositions, i.e., the systemic risk can be decomposed into risk due to individual agents.

Furthermore, one can associate a shadow price for systemic risk to each agent that correctly accounts for the externalities of the agent's individual decision-making on the entire system. Also, we provide a structural model for a financial network consisting of a set of firms holding common assets. In the model, endogenous asset prices are captured by the marketing clearing condition when the economy is in equilibrium. The key ingredients in the financial market that are captured in this model include the general portfolio choice flexibility of firms given posted asset prices and economic states, and the mark-to-market wealth of firms. The price sensitivity can be analyzed, where we characterize the key features of financial holding networks that minimize systemic risk, as a function of overall leverage. Finally, we propose a framework to estimate risk measures based on risk factors. By introducing a form of factor-separable risk measures, the acceptance set of the original risk measure connects to the acceptance sets of the factor-separable risk measures.

We demonstrate that the tight bounds for factor-separable coherent risk measures can be explicitly constructed.