It is widely held that financial systems, defined for example as the collection of banks and financial institutions in a developed country, can be modelled as a random network of nodes or vertices with stylized balance sheets, connected by directed links or edges that represent exposures ("interbank loans"), each edge with a positive weight that represents the size of the exposure. If ever a node becomes "insolvent" and ceases to operate as a bank, it will create balance sheet shocks to other nodes, creating the potential of chains of insolvency that we will call "default cascades".

Financial networks are difficult to observe because interbank data is often not publicly available, but studies have indicated that they share characteristics of other types of technological and social networks, such as the world wide web and Facebook. For example, the degree distributions of financial networks are thought to be "fat-tailed" since a significant number of banks are very highly connected. A less studied feature observed in financial networks (and as it happens, also the world wide web) is that they are highly "disassortative". This refers to the property that any bank's counterparties (i.e. their graph neighbours) have a tendency to be banks of an opposite character. For example, it is observed that small banks tend to link preferentially to large banks rather than other small banks. Commonly, social networks are observed to be assortative rather than disassortative. Structural characteristics such as degree distribution and assortativity are felt to be highly relevant to the propagation of contagion in networks but the nature of such relationships is far from clear.

The aim of our Systemic Risk Problem Solving Workshop is to develop mathematical frameworks that will be able to determine the systemic susceptibility in a rich class of random network models with enough flexibility to include the most important structural characteristics of real financial networks. Here is the original research description for our workshop: SFN.pdf

- My Lecture Notes from the 2012 Winter School on Financial Mathematics, Netherlands: Hours 1-3, Hours 4-5
- My Plenary Talk from Quantitative Methods in Finance Conference, Cairns, Australia, July 2012: QMF Talk
- Lionel's Report for
Ecole Polytechnique

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July 16-20, 2012)

- Prove the LTIA (locally treelike independence assumption) for the infinite assortative configuration model described in Hurd-Gleeson 2012.
- Study the accuracy of the LTIA approximation in real networks by
comparing the approximation to "exact" Monte Carlo simulations.

- Improve the stochastic modelling of a bank's balance sheet. That
is, go beyond the Gai-Haldane-Kapadia 2011 model, to better
capture the stylized facts of balance sheet transactions.

- Study a new network database for the EU banking system. EU Banking Networks

- Apply measures of systemic risk a la Amini-Cont-Minca 2011.
- Apply and extend the Watts type analytic framework of Cassier-Cheng-Hurd.
- Investigate policy alternatives that might reduce systemic risk
measures in a given system.