Abstracts

The recent financial crisis has demonstrated that systemic risk due to the interconnectedness of financial-market participants - such as financial institutions, insurers, governments and, even, regulators themselves - can dramatically amplify the consequences of isolated shocks to financial systems and pose a serious threat to prosperity and social stability. The traditional approach to risk control in financial mathematics is to apply risk measures to single institutions. However, this strategy fails to capture systemic risk because it treats institutions as if they were in isolation, and recent literature in financial mathematics has started to develop various approaches to rectify this deficiency in traditional risk management strategies. Some examples are the Conditional Value at Risk [Adrian and Brunnermeier, 2009] or the Conditional Expected Shortfall [Acharya et al., 2010] where the risk of the system, measured as the sum of the single institutions' P&L figures, is analyzed conditional on a stress scenario of a specific institution, or vice versa. However, while for a portfolio manager summing the single P&L figures is appropriate, this aggregation of risk factors might be problematic to measure systemic risk in a financial system. In [Chen et al., 2013] an axiomatic approach to (unconditional) risk measures for a system is introduced that considers more appropriate aggregation of risk factors than taking the sum. In our work we extend the approach in [Chen et al., 2013] along different lines. In particular, we will introduce and characterize conditional quasi-convex systemic risk measures that can be decomposed into a classical (conditional) risk measure applied to a (conditional) aggregation of risk factors. Further, we will consider consistency issues of such risk measures and discuss some examples. Also, contrary to [Chen et al., 2013] where a finite probability space is considered, we will work on a general probability space.