Date and LocationApr 06, 2018 - 1:00pm to 2:00pm
Systemic Risk in Financial Systems (presented by Pedro Cisneros, ECE Dept)
Eisenberg, L., & Noe, T. H. (2001). Systemic risk in financial systems. Management Science, 47(2), 236-249.
We consider default by firms that are part of a single clearing mechanism. The obligations of all firms within the system are determined simultaneously in a fashion consistent with the priority of debt claims and the limited liability of equity. We first show, via a fixed-point argument, that there always exists a “clearing payment vector” that clears the obligations of the members of the clearing system; under mild regularity conditions, this clearing vector is unique. Next, we develop an algorithm that both clears the financial system in a computationally efficient fashion and provides information on the systemic risk faced by the individual system firms. Finally, we produce qualitative comparative statics for financial systems. These comparative statics imply that, in contrast to single-firm results, even unsystematic, nondissipative shocks to the system will lower the total value of the system and may lower the value of the equity of some of the individual system firms.
Epidemic Processes over Time–Varying Networks (presented by David Grimsman, ECE Dept)
Paré, P. E., Beck, C. L., & Nedich, A. (2017). Epidemic processes over time-varying networks. IEEE Transactions on Control of Network Systems.
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can provide insights that lead to long-term societal benefits. Prior research has focused mainly on network models with static graph structures, however the systems being modeled typically have dynamic graph structures. In this paper, we consider virus spread models over networks with dynamic graph structures, and we investigate the behavior of these systems. We perform a stability analysis of epidemic processes over time–varying networks, providing sufficient conditions for convergence to the disease free equilibrium (the origin, or healthy state), in both the deterministic and stochastic cases. We present simulation results and discuss quarantine control via simulation.