Urn models and other approaches to risk and tails, with applications in risk management and climatology

This dissertation collects three scientific contributions, already published in international peer-reviewed journals, plus some extra considerations and work-in-progress. First, we present a model based on reinforced urn processes, which conjugates to the right-censored recovery process, and empirically apply it to the time series of recovery...

Predicting Stock Market Crashes using Urns and the Quantum Lorenz Ordering of Correlation Matrices

By sampling financial correlation matrices over sliding windows, it has been shown in recent work that the quantum majorization induced partial ordering on this space of correlation matrices known as the "quantum Lorenz ordering" (QLO) can be used to characterize systemic risk by clustering correlation matrices according to their degree...

An Urn-Based Nonparametric Modeling of the Dependence between PD and LGD with an Application to Mortgages

We propose an alternative approach to the modeling of the positive dependence between the probability of default and the loss given default in a portfolio of exposures, using a bivariate urn process. The model combines the power of Bayesian nonparametrics and statistical learning, allowing for the elicitation and the exploitation of experts’...

Computing the exact distributions of some functions of the ordered multinomial counts: Maximum, minimum, range and sums of order statistics

Starting from seminal neglected work by Rappeport (Rappeport 1968 Algorithms and computational procedures for the application of order statistics to queuing problems. PhD thesis, New York University), we revisit and expand on the exact algorithms to compute the distribution of the maximum, the minimum, the range and the sum of the J largest...