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

ISBN-10: 3642329020

ISBN-13: 9783642329029

ISBN-10: 3642329039

ISBN-13: 9783642329036

In this quantity contemporary advances within the use of contemporary quantitative versions for the research of assorted difficulties with regards to the dynamics of social and monetary platforms are provided. the bulk chapters describe instruments and methods of commonly perceived computational intelligence, significantly fuzzy common sense, evolutionary computation, neural networks and a few non-standard probabilistic and statistical analyses. as a result of the excessive complexity of the platforms and difficulties thought of, in lots of events it will be important to contemplate even as analytic, topological and statistical features and observe acceptable strategies and algorithms. This quantity is a right away results of shiny discussions held throughout the 5th foreign Workshop on Dynamics of Social and reasonably priced structures (DYSES) which used to be held at Benevento, Italy September 20-25, 2010, in addition to a number of post-workshop conferences and consultations.

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**Sample text**

For every bank i and for every j ∈ Niout ai j = M . |Niout | Proposition 1. If (ai j )i, j satisfies Assumptions 1,2,3, and |Niout | ≥ K ∗ = then it is resilient. RC − rC 1 − r(C − C ) L Networks of Financial Contagion 41 Proof. Let us assume that the exogenous shock strikes a bank j. Let K = |N out j |, ai j = a ji and L = ai j for each ai j = 0. By Assumption 2, K = |Niin |, so cj = x + ry + C KL x + ry + C M = . 1+M 1 + KL Since x = qC and Ry = (1 − q)C , then, for every i ∈ N in j , it follows that λi j = (1 − q)L(RC − rC ) =λ R(1 + KL) and b(q) = r (1 − q)(C − C ).

Cutillo, G. De Marco, and C. 3 Contagion When the contagion network F = ( fi j )i, j corresponds to the identity matrix then the default of any bank is not expected to spread to any other bank in the network. In the following we will refer to this property as the contagion resiliency of the interbank market: Definition 5. A network of interbank deposits A = (ai j )i, j is resilient from contagion if fi j = 1 if and only if i = j. It can be easily checked that if λi j ≤ b(q), for every pair of banks (i, j) with i = j, then the interbank market is resilient from contagion.

On the other hand, when n is even, h = n2 and the sets of h following and h preceding banks have a bank in common. The use of the term constant is improper because the adjacency matrix is not constant as ai j = 0 if and only if bank i is not directly linked to bank j and ai j = |NMout | otherwise. i 46 L. Cutillo, G. De Marco, and C. Donnini h ∈ {1, 2, 3, 4, 5}. Also in this case the contagion spread ranges from a full contagion (h = 1) to a diagonal contagion (h = 5). Note that the number of contagion links reduces dramatically as h grows.

### Advanced Dynamic Modeling of Economic and Social Systems by Myriam P. Sassano, Araceli N. Proto (auth.), Araceli N. Proto, Massimo Squillante, Janusz Kacprzyk (eds.)

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