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Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

We introduce a model in which a regulator employs mechanism design to embed her human capital beta signal(s) in a firm's capital structure, in order to enhance the value of her post career change indexed executive stock option contract with…

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

In this paper we propose a novel optimization framework to systematically solve robust PCA problem with rigorous theoretical guarantee, based on which we investigate very computationally economic updating algorithms.

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical…

Dynamical systems with components whose sizes evolve according to multiplicative stochastic rules have been recently combined with entry and exit processes. We show that the assumptions usually made in modeling exits are at odds with the…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

I study the optimal regulation of a financial sector where individual banks face self-enforcing constraints countering their default incentives. The constrained-efficient social planner can improve over the unregulated equilibrium in two…

The question of how to stabilize financial systems has attracted considerable attention since the global financial crisis of 2007-2009. Recently, Beale et al. ("Individual versus systemic risk and the regulator's dilemma", Proc Natl Acad…

We consider the problem of governing systemic risk in an assets-liabilities dynamical model of banking system. In the model considered each bank is represented by its assets and its liabilities.The capital reserves of a bank are the…

We develop a framework for price-mediated contagion in financial systems where banks are forced to liquidate assets to satisfy a risk-weight based capital adequacy requirement. In constructing this modeling framework, we introduce a…

The current global financial system forms a highly interconnected network where a default in one of its nodes can propagate to many other nodes, causing a catastrophic avalanche effect. In this paper we consider the problem of reducing the…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

The interconnectedness of financial institutions affects instability and credit crises. To quantify systemic risk we introduce here the PD model, a dynamic model that combines credit risk techniques with a contagion mechanism on the network…

We present a simple agent-based model of a financial system composed of leveraged investors such as banks that invest in stocks and manage their risk using a Value-at-Risk constraint, based on historical observations of asset prices. The…

Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank…

A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…

Central Counterparties (CCPs) are widely promoted as a requirement for safe banking with little dissent except on technical grounds (such as proliferation of CCPs). Whilst CCPs can have major operational positives, we argue that CCPs have…

We consider a model of contagion in financial networks recently introduced in the literature, and we characterize the effect of a few features empirically observed in real networks on the stability of the system. Notably, we consider the…