On the strategic origin of Brownian motion in finance

This paper is concerned with the strategic use of a private information on the stock market. A repeated auction model is used to analyze the evolution of the price system on a market with asymmetric information.  The model turns out to be a zero-sum repeated game with one-sided information, as introduced by Aumann and Maschler.  The stochastic evolution of the price system can be explicitly computed in the n times repeated case. As n grows to ∞, this process tends to a continuous time martingale related to a Brownian Motion.  This paper provides in this way an endogenous justification for the appearance of Brownian Motion in Finance theory. Received: February 2002     

A Numerical Approach of the sentinel method for distributed parameter systems

In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.      

Estimation de facteurs de Bayes entre modèles dynamiques non linéaires à espace d'état

The use of nonlinear state space models in the study and control of stochastic dynamic systems is regularly growing. With the new generation of particle filters, efficient filtering methods are now available for the identification of these models. However their statistical selection is still an open problem because of the frequent nonaccessibility of the related likelihoods and the intricate estimation of the latter. This rules out all the usual model comparison information criteria as Akaïke's and unfavour also the efficient methods relying on Bayes factor estimation by MCMC simulations.This Note shows how a convergent nonparametric Bayes factor estimator can be built and used advantageously, as direct application of these new particle filters themselves. To cite this article: J.-P. Vila, I. Saley, C. R. Acad. Sci. Paris, Ser. I 347 (2009).