A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling

In this paper we propose a new nonparametric approach to interacting failing systems (FS), that is systems whose probability of failure is not negligible in a fixed time horizon, a typical example being firms and financial bonds. The main purpose when studying a FS is to calculate the probability of default and the distribution of the number of failures that may occur during the observation period. A model used to study a failing system is defined default model. In particular, we present a general recursive model constructed by the means of inter- acting urns. After introducing the theoretical model and its properties we show a first application to credit risk modeling, showing how to assess the idiosyncratic probability of default of an obligor and the joint probability of failure of a set of obligors in a portfolio of risks, that are divided into reliability classes

Generalized extreme shock models with a possibly increasing threshold

We propose a generalized extreme shock model with a possibly increasing failure threshold. While standard models assume that the crucial threshold for the system may only decrease over time, because of weakening shocks and obsolescence, we assume that, especially at the beginning of the system's life, some strengthening shocks may increase the system tolerance to large shock. This is for example the case of turbines' running-in in the field of engineering. On the basis of parametric assumptions, we provide theoretical results and derive some exact and asymptotic univariate and multivariate distributions for the model. In the last part of the paper we show how to link this new model to some nonparametric approaches proposed in the literature

Microeconomic Structure determines Macroeconomic Dynamics. Aoki defeats the Representative Agent

Masanao Aoki developed a new methodology for a basic problem of economics: deducing rigorously the macroeconomic dynamics as emerging from the interactions of many individual agents. This includes deduction of the fractal / intermittent fluctuations of macroeconomic quantities from the granularity of the mezo-economic collective objects (large individual wealth, highly productive geographical locations, emergent technologies, emergent economic sectors) in which the micro-economic agents self-organize. In particular, we present some theoretical predictions, which also met extensive validation from empirical data in a wide range of systems: - The fractal Levy exponent of the stock market index fluctuations equals the Pareto exponent of the investors wealth distribution. The origin of the macroeconomic dynamics is therefore found in the granularity induced by the wealth / capital of the wealthiest investors. - Economic cycles consist of a Schumpeter 'creative destruction' pattern whereby the maxima are cusp-shaped while the minima are smooth. In between the cusps, the cycle consists of the sum of 2 'crossing exponentials': one decaying and the other increasing. This unification within the same theoretical framework of short term market fluctuations and long term economic cycles offers the perspective of a genuine conceptual synthesis between micro- and macroeconomics. Joining another giant of contemporary science - Phil Anderson - Aoki emphasized the role of rare, large fluctuations in the emergence of macroeconomic phenomena out of microscopic interactions and in particular their non self-averaging, in the language of statistical physics. In this light, we present a simple stochastic multi-sector growth model.Comment: 42 pages, 6 figure

GENERALIZED EXTREME SHOCK MODELS WITH A POSSIBLY INCREASING THRESHOLD

We propose a generalized extreme shock model with a possibly increasing failure threshold. Although standard models assume that the crucial threshold for the system might only decrease over time, because of weakening shocks and obsolescence, we assume that, especially at the beginning of the system's life, some strengthening shocks might increase the system tolerance to large shock. This is, for example, the case of turbines' running-in in the field of engineering. On the basis of parametric assumptions, we provide theoretical results and derive some exact and asymptotic univariate and multivariate distributions for the model. In the last part of the article we show how to link this new model to some nonparametric approaches proposed in the literatur

AN URN MODEL FOR CASCADING FAILURES ON A LATTICE

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial network

"Non-Self-Averaging in Macroeconomic Models: A Criticism of Modern Micro-founded Macroeconomics"

Using a simple stochastic growth model, this paper emonstrates that the coefficient of variation of aggregate output or GDP does not necessarily go to zero even if the number of sectors or economic agents goes to infinity. This phenomenon known as non-self-averaging implies that even if the number of economic agents is large, dispersion can remain significant, and, therefore, that we can not legitimately focus on the means of aggregate variables. It, in turn, means that the standard microeconomic foundations based on the representative agent has little value for they are expected to provide us with dynamics of the means of aggregate variables. The paper also shows that non-self-averaging emerges in some representative urn models. It suggests that non-self-averaging is not pathological but quite generic. Thus, contrary to the main stream view, micro-founded macroeconomics such as a dynamic general equilibrium model does not provide solid micro foundations.

Systems biology applications to study mechanisms of human immunodeficiency virus latency and reactivation

Eradication of human immunodeficiency virus (HIV) in infected individuals is currently not possible because of the presence of the persistent cellular reservoir of latent infection. The identification of HIV latency biomarkers and a better understanding of the molecular mechanisms contributing to regulation of HIV expression might provide essential tools to eliminate these latently infected cells. This review aims at summarizing gene expression profiling and systems biology applications to studies of HIV latency and eradication. Studies comparing gene expression in latently infected and uninfected cells identify candidate latency biomarkers and novel mechanisms of latency control. Studies that profiled gene expression changes induced by existing latency reversing agents (LRAs) highlight uniting themes driving HIV reactivation and novel mechanisms that contribute to regulation of HIV expression by different LRAs. Among the reviewed gene expression studies, the common approaches included identification of differentially expressed genes and gene functional category assessment. Integration of transcriptomic data with other biological data types is presently scarce, and the field would benefit from increased adoption of these methods in future studies. In addition, designing prospective studies that use the same methods of data acquisition and statistical analyses will facilitate a more reliable identification of latency biomarkers using different model systems and the comparison of the effects of different LRAs on host factors with a role in HIV reactivation. The results from such studies would have the potential to significantly impact the process by which candidate drugs are selected and combined for future evaluations and advancement to clinical trials