Ecole Normale Superieure

A Path Shadowing Monte-Carlo method provides prediction of future paths given any generative model.

At a given date, it averages future quantities over generated price paths whose past history matches, or “shadows”, the actual (observed) history.

We test our approach using paths generated from a maximum entropy model of financial prices,

based on the recently introduced “Scattering Spectra” which are multi-scale analogues of the standard skewness and kurtosis.

This model promotes diversity of generated paths while reproducing the main statistical properties of financial prices, including stylized facts on volatility roughness.

Our method yields state-of-the-art predictions for future realized volatility. It also allows one to determine conditional option smiles for the S&P500.

These smiles depend only on the distribution of the price process, and are shown to outperform both the current version of the Path Dependent Volatility model and the option market itself.

In the presence of a translation space-like Killing field

the 3 + 1 vacuum Einstein equations reduce to the 2 + 1

Einstein equations with a scalar field. We work in

generalised wave coordinates. In this gauge Einstein

equations can be written as a system of quaslinear

quadratic wave equations. The main difficulty is due to

the weak decay of free solutions to the wave equation in 2

dimensions. To prove long time existence of solutions, we

have to rely on the particular structure of Einstein

equations in wave coordinates. We also have to carefully

choose the behaviour of our metric in the exterior region

to enforce convergence to Minkowski space-time at

time-like infinity.

We will first review the return to equilibrium of the Ising model when a small external field is applied. The relaxation time is extremely long and can be estimated as the time needed to create critical droplets of the stable phase which will invade the whole system. We will then discuss the impact of disorder on this metastable behavior and show that for Ising model with random interactions (dilution of the couplings) the relaxation time is much faster as the disorder acts as a catalyst. In the last part of the talk, we will focus on the droplet growth and study a toy model describing interface motion in disordered media.

I propose to present modeling and experimental data about the organization of telomeres (ends of the chromosomes): the 32 telomeres in Yeast form few local aggregates. We built a model of diffusion-aggregation-dissociation for a finite number of particles to estimate the number of cluster and the number of telomere/cluster and other quantities. We will further present based on eingenvalue expansion for the Fokker-Planck operator, asymptotic estimation for the mean time a piece of a polymer (DNA) finds a small target in the nucleus.