This page contains some lecture notes about courses I had the opportunity to teach in the past.

Modelling anticipations on a financial market Princeton University, 2003

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This course was given in Princeton University in 2003, where I was invited by Patrick Cheridito. It is intended to graduate, post graduate students. These notes were published (in a  different form) by Springer: In Paris-Princeton Lectures on Mathematical Finance, LNM 1814, (2003).

Financial markets obviously have asymmetry of information. That is, there are different type of traders whose behavior is induced by different types of information that they possess. Let us consider a "small" investor who trades in a arbitrage free financial market so as to maximize the expected utility of his wealth at a given time horizon. We assume that he possesses extra information about the future price of a stock. Our basic question is: What is the value of this information ?



Basic probability theory Ho Chi Minh city, 2006

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This course was given in Vietnam in January 2006. It is a first course in probability theory. The notes are a bit rough but were useful to the students.




Stochastic calculus In French, Toulouse University, 2004-2007

Le mouvement brownien est un processus stochastique omniprésent en théorie des probabilités. Il fut étudié au début du siècle par Bachelier, Einstein et Wiener. Dans les années quarante, Ito s'en sert pour développer un calcul stochastique permettant de résoudre des équations différentielles perturbées aléatoirement.

Le calcul stochastique est un mariage de la théorie des probabilités et du calcul différentiel et intégral, qui a trouvé depuis beaucoup d'applications (équations aux dérivées partielles, géométrie différentielle, mathématiques financières, télécommunications, etc...). Dans ce cours, nous présentons le mouvement brownien et le calcul stochastique qui lui est associé. L'accent est mis sur la théorie des diffusions.


Chapitre 0: Quelques rappels de théorie des probabilités

Chapitre 1: Processus stochastiques

Chapitre 2: Martingales

Chapitre 3: Mouvement brownien

Chapitre 4: Calcul d'Itô



Stochastic Taylor expansions and heat kernel asymptotics, Spring School of Mons, June 2009

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These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these methods we provide a new heat kernel proof of the Chern-Gauss-Bonnet theorem.