6 EC
Semester 1, period 1, 2
5334ATIS6Y
| Owner | Master Mathematics |
| Coordinator | dr. A. Khedher |
| Part of | Master Mathematics, year 1Master Stochastics and Financial Mathematics, year 1 |
The central theme of this course is backwards stochastic differential equations (BSDEs). These are stochastic differential equations for which not the initial, but the final value is given. Although this seems like a small difference, the implications are severe as the solution must satisfy adaptivity conditions.The motivation for studying BSDEs comes from, e.g., stochastic control and hedging problems in finance. Another application lies in the link between BSDEs and non-linear PDEs, given by the extension of a Feynman-Kac formula.
Topics that are covered in this course are:- well-posedness of BSDEs with Lipschitz coefficients- the relation between BSDEs and (deterministic) PDEs- examples of BSDEs arising from applications- Malliavin calculus: this involves the question of taking derivatives with respect to a Brownian motion and allows us to analyse the regularity of a (B)SDE.- approximation of BSDEs by numerical methods-well-posedness of BSDEs with quadratic coefficients.
lecture notes for the first part of the lecture and slides for the second part (made available at the first lecture)
David Nualart, ' The Malliavin Calculus and Related Topics', Springer, ISBN 978-3-540-28329-4 (not necessary to buy this).
Huyên Pham, 'Continuous-time stochastic control and optimization with financial applications', Springer, ISBN 978-3-540-89500-8 (not necessary to buy this)
https://www.sciencedirect.com/science/article/pii/S0304414904000031
|
Activity |
Hours |
|
|
Hoorcollege |
28 |
|
|
Oral exam |
1 |
|
|
Self study |
139 |
|
|
Total |
168 |
(6 EC x 28 uur) |
The programme does not have requirements concerning attendance (OER-B).
| Item and weight | Details |
|
Final grade | |
|
60% Oral exam | |
|
40% Assignments |
There will be an oral exam for each part of the course. Sonja Cox will give an oral exam for the first part of the course. Asma Khedher will give an oral exam for the second part of the course. To have the exam, you make an appointment with the lecturers.
What do you have to know? The theory and homework, i.e. all important definitions and results (lemma's, theorems, etc.). The details about which theory will be discussed two weeks prior to the exam.
The final grade is a combination of the results of the take home assignments (which counts 40 %) and the first and second oral exam (together 60%). To pass the course the average grade of both oral exams should be higher than 5.0.
During the course, the students will have to hand in a total of six sets of homework. The assignments will contain theoretical and numerical exercises. The average homework grade will count for 40% in the final grade
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl
| Weeknummer | Onderwerpen | Studiestof |
| 1 | Stochastic integration recapitulation | Chapter 1 (first take home assignment) |
| 2 | Introduction and well posedness of BSDEs | Chapter 2, Sections 2.1-2.2 |
| 3 | Relation between BSDEs and non-linear PDEs | Chapter 2, Sections 2.3-2.5 (second take home assignment and deadline of the first one) |
| 4 | Wiener-chaos decomposition | Chapter 3, Section 3.1 |
| 5 | Malliavin derivative | Chapter 3, Section 3.2 (third take home assignment and deadline of the second one) |
| 6 | Divergence operator | Chapter 3, Section 3.3 |
| 7 | Malliavin calculus for SDEs | Chapter 3, Section 3.4 (deadline for the third take home assignment) |
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| 16 |
The schedule for this course is published on DataNose.