Technische
Universitat Berlin - TU-Berlin
Faculty
of Mathematics
-
Backward Stochastic Differential Equations and applications
- WiSe 2012/13
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-
General information -- Latest update: 15.Feb.2013 09:30
- Timeplan:
- Friday 10:00 - 12:00, Room E-N 195 (TU-Berlin); from
19.Okt.2012 until 15.Feb.2013
- Prerequisite:
- Probability Theory I,II (Stochastik I,II)
- Exams:
- 30 to 45 mins oral exam at end of semester
-
- Registration required!!!
- Oral exam days: 28/Feb and 4/Apr
- Other remarks
- This is an BMS Advanced Course, it will be held in English!
- This course is worth 5 Credits
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Literature
- List of relevant literature
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Content/summary of the classes
- 19.Okt
- General introduction; Class details
- 26.Okt
- Chp 1.0: Notations and definitions
- Chp 2.0: Lipschitz BSDEs
- Sec 2.1: Introduction: Why do BSDEs look like BSDEs?
- Sec 2.2: Martingale Representation Theorem (MRT)
- Sec 2.3: Basic BSDEs, solutions via MRT
- 02.Nov
- Sec 2.3: Linear BSDEs - change of drift and measure; computable solutions; problems
- Sec 2.4: Lipschitz BSDE - Def. of Solution; Standard data; preparation for main result
- 09.Nov
- Sec 2.4: Lipschitz BSDEs - existence and uniqueness results
- 16.Nov
- Sec 2.4: Closing remarks - patching and the small time interval argument
- Sec 2.5: Lipschitz BSDEs - comparison and corollaries
- linear transformation, boundedness, positivity
- 23.Nov
- Sec 2.5: Dependence on initial data and Lp estimates; closing remarks
- Chp 3.0: Forward-Backward SDE or FBSDEs
- Sec 3.0: Introduction / Recalls on SDE theory
- 30.Nov
- No class (teacher was sick)
- 07.Dez
- Sec 3.1: Recalls on SDE theory (exist., uniq., stability)
- SubSec 3.1.1: The linear Feynman-Kac formula
- Sec 3.2: FBSDEs: Existence, uniqueness and other properties
- SubSec 3.2.1: PDEs to FBSDEs - The non-linear Feyman-Kac Formula
- 14.Dez
- SubSec 3.2.2: Regularities of FBSDEs (I)
- 21.Dez
- No class this week - to be rescheduled
- 11.Jan
- SubSec 3.2.3: FBSDEs to PDEs - Viscosity solutions and FBSDEs
- 18.Jan
- SubSec 3.2.4: Regularities of FBSDEs (II) - The Z component
- 25.Jan
- SubSec 3.2.4: Regularities of FBSDEs (II) - The Z component (continued)
- Sec 3.3: Time discretization of FBSDEs
- SubSec 3.3.1: Euler Scheme for SDEs
- SubSec 3.3.2: Backward Euler Scheme for the BSDE
- SubSec 3.3.3: Expectations and Monte Carlo
- 28.Jan
- Chp 4.0: Two other classes of BSDEs
- Sec 4.1: Quadratic growth BSDEs
- 01.Feb
- Sec 4.1: Quadratic growth BSDEs (continued)
- 08.Feb
- Sec 4.2: Fully coupled FBSDEs
- SubSec 4.2.1: Fun with 1-D parabolic Burgers with damping
- Time reversion, PDE perturbation, limit procedure
- SubSec 4.2.2: Fully coupled FBSDEs;
- Existence & Counter-examples
- 15.Feb
- Overview and discussion