Stochastic Differential Equations (3TU Mastermath 2010-2011)This
link contains the solutions of the written exam.
Lecturers: Jan van Neerven (lectures 1-8) and Arun Bagchi (lectures 9-12) Course book: J. M. Steele: 'Stochastic Calculus and Financial Applications', Springer, 2001. The exam covers the chapters 1, 2, 3, 4, 6, 7, 8, 9, and 13 (sections 13.1-13.5), along with the material of this handout. Venue: Buys Ballot Lab, room BBL 079, Utrecht. Time: Mondays at 10.15 Lecture 1: 7-2 (Recap: Measure and Integration Theory; handout and [Steele 4.1]) Exercises for week 1 Lecture 2: 14-2 (Conditional Expectations; handout and [Steele 4.2]) Exercises for week 2 Lecture 3: 28-2 (Discrete martingales; [Steele 2.1-2.5]) Exercises for week 3 Lecture 4: 7-3 (Martingale convergence and continuous martingales; [Steele 2.6, 4,3.4.4]) Exercises for week 4 Lecture 5: 14-3 (Brownian motion; [Steele 3.1-3.5, 4.5]) Exercises for week 5 Lecture 6: 21-3 (Stochastic integration; [Steele 6.1-6.4]) Exercises for week 6 Lecture 7: 28-3 (Localisation; [Steele 6.5, 7.1-7.3]) Exercises for week 7 Lecture 8: 18-4 (Local martingales; [Steele 7.4-7.5]) (There will be no exercises for week 8) Lecture 9: 2-5 (Ito formula; [Steele 8]) Exercises for week 9; Solutions Lecture 10: 9-5 (Stochastic differential equations; [Steele 9]) Exercises for week 10; Solutions Lecture 11: 16-5 (Stochastic differential equations; [Steele 9] Lecture 12: 23-5 (Girsanov theorem; [Steele 13.1-13.5]) Slides on Girsanov; Exercise with solution More information can be found on the Mastermath website. |