I will discuss the behavior of N bosons trapped in a potential well subject
to a pairwise interaction. In the mean-field limit -- i.e., when N tends to
infinity while keeping the interaction per particle bounded -- the evolution
of a product state remains, asymptotically, a product state. The single
particle wave-function then evolves according to a non-linear Hartree
equation. Versions of this result have been proved before, e.g., by
Hepp in 1977, Spohn in 1980 or, recently, by Rodnianski and Schlein, but
the proofs are often quite technically involved. I will describe a very simple,
and ideologically correct, proof (for bounded interaction potentials) based
on exchengeability and Stormer's (aka quantum deFinetti) theorem.
Based on recent discussions with Nick Crawford.

The two main approaches to modeling defaults, structural and intensity based, will be reviewed. We show that perturbation methods are useful in approximating default probabilities in the context of stochastic volatility models. We then consider the case of many names and we discuss various ways of creating correlation of defaults. In highly-dimensional models, Monte Carlo simulations remain a powerful tool for computing prices of credit derivatives such as CDO's tranches and associated greeks. We propose an interactive particle system approach for computing the small probabilities involved in these financial instruments.