The recursive prediction and filtering formulas of the Kalman filter are difficult to implement in nonlinear state space models since they require the updating of a function. The aim of this paper is to consider the situation of a large number n of individual measurements, called...

We consider a homogeneous class of assets, whose returns are driven by an unobservable factor representing systematic risk. We derive approximated pricing formulas for the future factor values and their proxies, when the size n of the class is large. Up to order 1/n, these closed-form...

In this article we explain how to use rating histories provided by the internal scoring systems of banks and rating agencies in order to predict the future risk of a set of borrowers. The method is developed following the steps suggested by the Basle Committee. To introduce both migration...

The recursive prediction and filtering formulas of the Kalman filter are difficult to implement in nonlinear state space models since they require the updating of a function. The aim of this paper is to consider the situation of a large number n of individual measurements, called...