Les scores de la Banque de France : leur développement, leurs applications, leur maintenance.

diagnostic d’entreprise, risque de crédit, credit scoring, probabilité de défaillance, défaut de paiement, classes de risque, maintenance des scores.

On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations

We consider the Euler equations in a three-dimensional Gevrey-class bounded domain. Using Lagrangian coordinates we obtain the Gevrey-class persistence of the solution, up to the boundary, with an explicit estimate on the rate of decay of the Gevrey-class regularity radius

Semiclassical Theory of Time-Reversal Focusing

Time reversal mirrors have been successfully implemented for various kinds of waves propagating in complex media. In particular, acoustic waves in chaotic cavities exhibit a refocalization that is extremely robust against external perturbations or the partial use of the available information. We develop a semiclassical approach in order to quantitatively describe the refocusing signal resulting from an initially localized wave-packet. The time-dependent reconstructed signal grows linearly with the temporal window of injection, in agreement with the acoustic experiments, and reaches the same spatial extension of the original wave-packet. We explain the crucial role played by the chaotic dynamics for the reconstruction of the signal and its stability against external perturbations.Comment: 4 pages, 1 figur

Hilbert Expansion from the Boltzmann equation to relativistic Fluids

We study the local-in-time hydrodynamic limit of the relativistic Boltzmann equation using a Hilbert expansion. More specifically, we prove the existence of local solutions to the relativistic Boltzmann equation that are nearby the local relativistic Maxwellian constructed from a class of solutions to the relativistic Euler equations that includes a large subclass of near-constant, non-vacuum fluid states. In particular, for small Knudsen number, these solutions to the relativistic Boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic Euler equations.Comment: 50 page

La contagion du risque via les impayés sur effets de commerce.

Le crédit interentreprises est un des canaux de transmission du risque de défaillance des entreprises. Les impayés sur effets de commerce révèlent les interdépendances entre secteurs et leur potentiel de contagion, dès lors que les montants en jeu sont importants.contagion, diffusion du risque, estimateur par appareillement, taux de défaut, probabilité de défaut, impayés, incidents de paiement, effets de commerce, crédit interentreprises, solde commercial.

Macro stress testing with a macroeconomic credit risk model: Application to the French manufacturing sector.

The aim of this paper is to build and estimate a macroeconomic model of credit risk for the French manufacturing sector. This model is based on Wilson's CreditPortfolioView model (1997a, 1997b); it enables us to simulate loss distributions for a credit portfolio for several macroeconomic scenarios. We implement two simulation procedures based on two assumptions relative to probabilities of default (PDs): in the first procedure, firms are assumed to have identical default probabilities; in the second, individual risk is taken into account. The empirical results indicate that these simulation procedures lead to quite different loss distributions. For instance, a negative one standard deviation shock on output leads to a maximum loss of 3.07% of the financial debt of the French manufacturing sector, with a probability of 99%, under the identical default probability hypothesis versus 2.61% with individual default probabilities.macro stress test ; credit risk model ; loss distribution.

Inviscid Large deviation principle and the 2D Navier Stokes equations with a free boundary condition

Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces

Mean-field evolution of fermions with singular interaction

We consider a system of N fermions in the mean-field regime interacting though an inverse power law potential $V(x)=1/|x|^{\alpha}$, for $\alpha\in(0,1]$. We prove the convergence of a solution of the many-body Schr\"{o}dinger equation to a solution of the time-dependent Hartree-Fock equation in the sense of reduced density matrices. We stress the dependence on the singularity of the potential in the regularity of the initial data. The proof is an adaptation of [22], where the case $\alpha=1$ is treated.Comment: 16 page

Blow-up of the hyperbolic Burgers equation

The memory effects on microscopic kinetic systems have been sometimes modelled by means of the introduction of second order time derivatives in the macroscopic hydrodynamic equations. One prototypical example is the hyperbolic modification of the Burgers equation, that has been introduced to clarify the interplay of hyperbolicity and nonlinear hydrodynamic evolution. Previous studies suggested the finite time blow-up of this equation, and here we present a rigorous proof of this fact

Empirical estimation of the option premium for residential redevelopment

This paper presents and validates a novel empirical approach for measuring the value of the option to redevelop using a standard hedonic dataset. Our analysis generalizes the standard hedonic model to account for the option value of reconfiguring hedonic characteristics. We test this model with over 162,000 real estate transactions in 53 towns in Connecticut between 1994 and 2007 by adding a non-linear intensity variable, which increases with the aggregate value of structure and decreases with land value. A conservative estimate is that about 20% of towns have significantly positive option value, with a mean value of 29–34% for properties most similar to vacant land. Multiple tests across towns support predictions of real options theory. Positive option value towns have higher house price volatility and estimated option value varies positively with price volatility, a finding inconsistent with NPV theory. We also find positive association between option value and drift in house prices and a U-shape relation with house price adjusted for structural characteristics. Higher property taxes reduce the value of option to redevelop