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Bootstrapping topology and systemic risk of complex network using the fitness model

We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network density and the degree distri- bution as a function of the size of the initial subset of nodes.

The Evolution of Complex Networks: A New Framework

We introduce a new framework for the analysis of the dynamics of networks, based on randomly reinforced urn (RRU) processes, in which the weight of the edges is determined by a reinforcement mechanism. We rigorously explain the empirical evidence that in many real networks there is a subset of "dominant edges" that control a major share of the total weight of the network. Furthermore, we introduce a new statistical procedure to study the evolution of networks over time, assessing if a given instance of the nework is taken at its steady state or not.

Topologically biased random walk and community finding in networks

We present an approach of topology biased random walks for undirected networks. We focus on a one-parameter family of biases, and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion to study the features of random walks vs parameter values. Furthermore, we show an analysis of the spectral gap maximum associated with the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state.

Non-Gaussian Price Dynamics and Implications for Option Pricing

It is well known that the probability distribution of stock returns is non-gaussian. The tails of the distribution are too “fat”, meaning that extreme price movements, such as stock market crashes, occur more often than predicted given a gaussian model. Numerous studies have attempted to characterize and explain the fat-tailed property of returns. This is because understanding the probability of extreme price movements is important for risk management and option pricing. In spite of this work, there is still no accepted theoretical explanation.

Evolution of controllability in interbank networks

The present economic downturn has revealed an unexpected com- plexity of financial markets and brought to the fore new questions both to scientists and regulators. Institutions of heterogeneous size get connected in complex networks of financial ties which play a major role for the spread of contagion. The current debate in reg- ulation focuses on how to identify systemically important financial institutions, as well as on how many and which institutions should be monitored by central banks.

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