Abstracts

We define systemic risk measures for a network of interconnected banks to be the risk of the system to the obligations the financial firms have to the outside economy. Since the value that is of interest to a regulator is not the acceptable level of impact to the outside economy, but rather the capital requirements for each financial firm which makes the overall system acceptable, it is natural to consider systemic risk measures as set-valued risk measures. We will model the financial system via a network of obligations, as introduced by Eisenberg and Noe (2001), but with random endowments for each firm. In order to measure the systemic risk and create the valuations for each firm, we will introduce random stresses into the system to find the fixed-point payment structure in the network model (as a random vector). We use these clearing payments to measure the risk of the system via the resultant outcome for the outside economy. Additionally, various allocation mechanisms are discussed which can be used to define the optimal capital requirements with financial interpretations. Finally, case studies with differing network structures and stress scenarios are run to compare the acceptable capital allocations for the network of firms.