Stochastic Integration - M2 - 8EC

1) Prerequisites

Measure theory, stochastic processes at the level of the course measure theoretic probability, see lecture notes https://staff.fnwi.uva.nl/p.j.c.spreij/onderwijs/master/mtp.pdf written by Peter Spreij

2) Aim of the course

  • the 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

This course includes optional homework assignments and a final written examination. The homework is intended as practice and will not contribute to the final grade. The final grade will be based entirely on the final written exam (or, if applicable, the 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.c.spreij/onderwijs/master/si.pdf

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.