1) Prerequisites:
Measure theory, stochastic processes at the level of the course measure theoretic probability, see lecture notes https://staff.fnwi.uva.nl/s.g.
2) Aim of the course:
- he students can explain the theory and construction of stochastic integrals,
- the students are able to apply the Ito formula,
- the students can explain different solution concepts of SDEs, students know how to apply measure changes for continuous semimartingales (Girsanov's theorem) and are able to calculate the new drift,
- the students are able to compare SDEs and PDEs, and can calculate the probabilistic representation of solutions to PDEs,
- the students are able to solve problems, where knowledge of the above topics is essential.
3) Rules about Homework/Exam:
Homework. Compulsory take home assignments! Strict deadlines: although serious excuses will always be accepted. You are allowed to work in pairs (a pair means 2 persons, not 3 or more), in which case one set of solutions should be handed in. Examination. The final grade is a combination of the results of the take home assignments and the written exam. The homework results count for 30% of the final grade and the written exam counts for 70%. To pass the exam, the final grade should be equal to or higher than 5,6 AND the grade for the written exam should be higher than 5,0.
Depending on the number of students, the retake could be an oral exam. The homework still counts 30% of the final grade in the case of a retake.
4) Lecture notes/Literature:
The course is based on the lecture notes by Peter Spreij, which will be distributed via the MasterMath ELO. They can also be found on Peter Spreij's homepage: https://staff.fnwi.uva.nl/p.j.
Recommended background reading:
- I. Karatzas and S.E. Shreve, Brownian motions and stochastic calculus,
- D. Revuz and M. Yor, Continuous martingales and Brownian motion.
These books form the main basis for the lecture notes that we use for the course.
5) Lecturers:
Asma Khedher
Gergely Bodo
- Docent: Gergely Bodo
- Docent: Asma Khedher