Covariance matrix filtering with bootstrapped hierarchies.

Cleaning covariance matrices is a highly non-trivial problem, yet of central importance in the statistical inference of dependence between objects. We propose here a probabilistic hierarchical clustering method, named Bootstrapped Average Hierarchical Clustering (BAHC), that is particularly effective in the high-dimensional case, i.e., when there are more objects than features. When applied to DNA microarray, our method yields distinct hierarchical structures that cannot be accounted for by usual hierarchical clustering. We then use global minimum-variance risk management to test our method and find that BAHC leads to significantly smaller realized risk compared to state-of-the-art linear and nonlinear filtering methods in the high-dimensional case. Spectral decomposition shows that BAHC better captures the persistence of the dependence structure between asset price returns in the calibration and the test periods.

Statistically validated network of portfolio overlaps and systemic risk.

Common asset holding by financial institutions (portfolio overlap) is nowadays regarded as an important channel for financial contagion with the potential to trigger fire sales and severe losses at the systemic level. We propose a method to assess the statistical significance of the overlap between heterogeneously diversified portfolios, which we use to build a validated network of financial institutions where links indicate potential contagion channels. The method is implemented on a historical database of institutional holdings ranging from 1999 to the end of 2013, but can be applied to any bipartite network. We find that the proportion of validated links (i.e. of significant overlaps) increased steadily before the 2007-2008 financial crisis and reached a maximum when the crisis occurred. We argue that the nature of this measure implies that systemic risk from fire sales liquidation was maximal at that time. After a sharp drop in 2008, systemic risk resumed its growth in 2009, with a notable acceleration in 2013. We finally show that market trends tend to be amplified in the portfolios identified by the algorithm, such that it is possible to have an informative signal about institutions that are about to suffer (enjoy) the most significant losses (gains).

Emergence of heterogeneity in a noncompetitive resource allocation problem.

Tuning one's shower in some hotels may turn into a challenging coordination game with imperfect information. The temperature sensitivity increases with the number of agents, making the problem possibly unlearnable. Because there is in practice a finite number of possible tap positions, identical agents are unlikely to reach even approximately their favorite water temperature. We show that a population of agents with homogeneous strategies is evolutionary unstable, which gives insights into the emergence of heterogeneity, the latter being tempting but risky.

Bug propagation and debugging in asymmetric software structures.

We address the issue of how software components are affected by the failure of one of them, and the inverse problem of locating the faulty component. Because of the functional form of the incoming link distribution of software dependence network, software is fragile with respect to the failure of a random single component. Locating a faulty component is easy if the failure only affects its nearest neighbors, while it is hard if it propagates further.

Criticality and market efficiency in a simple realistic model of the stock market.

We discuss a simple model based on the minority game which reproduces the main stylized facts of anomalous fluctuations in finance. We present the analytic solution of the model in the thermodynamic limit. Stylized facts arise only close to a line of critical points with nontrivial properties, marking the transition to an unpredictable market. We show that the emergence of critical fluctuations close to the phase transition is governed by the interplay between the signal to noise ratio and the system size. These results provide a clear and consistent picture of financial markets, where stylized facts and verge of unpredictability are intimately related aspects of the same critical systems.

Optimal combinations of imperfect objects.

We consider how to make best use of imperfect objects, such as defective analog and digital components. We show that perfect, or near-perfect, devices can be constructed by taking combinations of such defects. Any remaining objects can be recycled efficiently. In addition to its practical applications, our "defect combination problem" provides a novel generalization of classical optimization problems.