Stochastic calculus  -  13 lectures+exercice sessions

Chap 1: Stochastic processes
Chap 2: Brownian Motion
Chap 3: Continuous time martingales
Chap 4: Stochastic Integral
Chap 5: Stochastic Differential Equations.


(few) References :

-   Jean-Francois Le Gall, Mouvement brownien, martingales et calcul stochastique, Mathématiques et Applications, https://doi-org.ezproxy.universite-paris-saclay.fr/10.1007/978-3-642-31898-6
(also handout of Prof. Le Gall lecture easy to find on google)

-  Damien Lamberton and Bernard Lapeyre, Introduction to Stochastic Calculus Applied to Finance , Edition 2nd Edition, First Published 2007, Pub. Location New York, Imprint Chapman and Hall/CRC
DOI https://doi.org/10.1201/9781420009941

-  Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Series Title Graduate Texts in Mathematics, https://doi.org/10.1007/978-1-4612-0949-2

-  F. Comets and Thierry Meyre – Calcul stochastique et modèles de diffusions : Cours et exercices corrigés, Dunod, 2006, Coll. Sciences, sup. iii


Tentative schedule :

1. Lectures  Stoch Process
2. Exercice  Stoch Process
3. Lecture   Brownian Motion
4. Lecture   Brownian Motion / Exercice BM
5. Exercice  B.M.
6. Lecture   Continuous time martingale
7. Exercice  Continuous time martingale
8. Lecture   Stochastic Integral
9. Lecture   Stochastic Integral / Exercice Stochastic Integral
10 Exercice  Stochastic Integral
11 Exercice  Stochastic Integral / Lecture Stochastic Differential Equation
12 Lecture   S.D.E.
13 Exercice  S.D.E.