## Instructor:

## Semester:

- 2017 Spring/Summer (Jan - May)

Course Content:

Probability: Conditional expectations, martingales, Brownian motion, stochastic calculus,

Finance: Discrete derivatives pricing theory, continuous time pricing theory, stochastic volatility models, partial differential equations in finance,

Research topics: Martingale optimal transport problem, Systemic risk, etc.

Main texts:

1. Stochastic Calculus and Financial Applications, Michael Steele

2. The Mathematics of Arbitrage, Delbaen and Schachermayer

3. Stochastic Calculus for Finance, Volume 1 and 2. Steven Shreve

Reference Books:

1. Brownian Motion and Stochastic Calculus by Ioannis Karatzas and Steven E. Shreve Springer-Verlag, New York Second Edition, 1991.

2. Essentials of Stochastic Finance, Albert Shiryaev

3. Martingale methods in Financial Modeling, M. Musiela and M. Rutkowski, Springer, 1998.

4. Methods of Mathematical Finance by Ioannis Karatzas and Steven E. Shreve Springer-Verlag, New York 1998