Course title: Stochastic processes for finance  
Teacher: B. De Meyer
E-mail:  [email protected]
UE 2
Major(s): FQ
ECTS: 5
Evaluation: written and/or oral exam
Prerequisites: Introduction to Stochastic calculus

Presentation:
Local martingales and semimartingales will be introduced and the integral with respect to these processes  will be defined.
Details of the sessions:

1. 1) Local Martingales, semi martingales and their quadratic variation
   2) Itô’s integral with respect to a semi-martingale
   3) General Itô’s formula
   4) Levy’s characterization of the Brownian motion
   5) The link between PDE and stochastic processes (Montecarlo methods)
   6) Girsanov Theorem and application to finance (Black and Scholes formula) 
   7) Predictable representation property

References:

• Revuz, D., M. Yor, Continuous Martingales and Brownian Motion, Springer 2005.
• Karatzas, I., S. Shreve, Brownian Motion and Stochastic Calculus, 2nd. ed., Springer 1991.

Lamberton, D., B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, 2nd. Ed., Chapman and Hall, 2007.