By Myriam P. Sassano, Araceli N. Proto (auth.), Araceli N. Proto, Massimo Squillante, Janusz Kacprzyk (eds.)

In this quantity fresh advances within the use of contemporary quantitative versions for the research of assorted difficulties relating to the dynamics of social and financial platforms are provided. the bulk chapters describe instruments and strategies of generally perceived computational intelligence, significantly fuzzy good judgment, evolutionary computation, neural networks and a few non-standard probabilistic and statistical analyses. as a result of excessive complexity of the platforms and difficulties thought of, in lots of occasions it is crucial to think about while analytic, topological and statistical facets and observe applicable strategies and algorithms. This quantity is an immediate results of shiny discussions held throughout the 5th overseas Workshop on Dynamics of Social and within your budget platforms (DYSES) which was once held at Benevento, Italy September 20-25, 2010, in addition to a few post-workshop conferences and consultations.

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In order to focus to the systemic risk of financial contagion, the analysis is usually restricted to interbank markets insured against liquidity shocks. 1 Contagion Threshold Losses Given Default Suppose that an exogenous shock leads to the default of bank j and there are no other liquidity shocks 4 . Then, the other banks will be trying to withdraw their claims on the bank j and, at the same time the bank j liquidates its deposits in the other banks. All depositors must be treated equally; that is, every depositor gets the same liquidation value c j from the bank j for each unit invested at the first date, whether the depositor is a consumer or another bank.

In this way we have a problem similar to the optimization problem (20) in Allen and Gale (1998). So, under the condition x ≤ Ry, the optimal portfolio is (x, y) = qC , 1−q C R . (3) Networks of Financial Contagion 35 In our work we will retain (3) as first best. Interbank Market Even if a bank chooses the first best allocation at time t = 0 the realization of a state s at time t = 1 causes either a liquidity surplus, a liquidity shortage or the bank can perfectly meet withdrawals from early consumers.

36 L. Cutillo, G. De Marco, and C. Donnini which, obviously, implies that 1 − x − y ≥ 0. For the sake of simplicity, we consider only networks such that ∑ j∈N ai j = ∑ j∈N a ji , for every bank i. Moreover, as previously observed, at time t = 1, when the real state of nature s is revealed, each bank i incurs either a liquidity surplus (pi (s) − q < 0), a liquidity shortage (pi (s) − q > 0) or the bank can perfectly meet withdrawals from early consumers (pi (s) − q = 0). In order to honor the contracts concluded with consumers and to redeem deposits to the other banks, a bank i that incurs a liquidity shortage needs to withdraw its deposits.

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