Technische Universitat Berlin - TU-Berlin
Faculty of Mathematics

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Backward Stochastic Differential Equations and applications - WiSe 2012/13


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

Literature

List of relevant literature

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


G. dos Reis homepage Research Conferences and Talks Teaching CV & related