Course title: Stochastic calculus 2 (Calcul stochastique 2)
Teacher: B. De Meyer
E-mail: demeyer@univ-paris1.fr
UE 2
Major(s): FQ
ECTS: 5
Evaluation: written and/or oral exam
Prerequisites: Stochastic calculus 1
Presentation:
Local martingales and semimartingales will be introduced and the integral with respect to these processes will be defined.
Details of the sessions:
)
Teacher: B. De Meyer
E-mail: demeyer@univ-paris1.fr
UE 2
Major(s): FQ
ECTS: 5
Evaluation: written and/or oral exam
Prerequisites: Stochastic calculus 1
Presentation:
Local martingales and semimartingales will be introduced and the integral with respect to these processes will be defined.
Details of the sessions:
- 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
- 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.
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