#
Probability III (Stat GR6303) - Fall 2017

This course is for PhD students only.

*Instructor:* Marcel Nutz
*Meeting time:* Tuesdays and Thursdays 8:40-9:55, Room 520 Math
- Office
hours: Thursdays 11:25-12:15, Rooms 520 Math/910 SSW

This
course is an advanced introduction to stochastic control, dynamic
programming, viscosity solutions of nonlinear parabolic PDEs and
backward stochastic differential equations (BSDEs) with examples from
mathematical finance. It is based on the following lecture notes:

- N. Touzi (2013), Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE. Fields Institute Monographs No. 29, Springer Verlag, New York. DOI: 10.1007/978-1-4614-4286-8.

You can download the eBook from the publisher's website (licensed through Columbia's library services).

Prerequisites: Probability I
and II. This will be a fast-paced lecture; students are expected to
have some maturity in real analysis, probability theory and stochastic
analysis (Ito calculus). Knowledge of PDEs is not required but
some prior exposure may be helpful.

Additional reading with more examples: H. Pham (2009), Continuous-time Stochastic Control and Optimization with Financial Applications, Springer Verlag, New York (link).
## Contents

- Conditional Expectation and Linear Parabolic PDEs
- Stochastic Control and Dynamic Programming
- Optimal Stopping
- Solving Control Problems by Verification
- Viscosity Solutions
- Dynamic Programming Equation in the Viscosity Sense
- Backward SDEs and Stochastic Control
- Quadratic Backward SDEs