# Financial Mathematics

### When/Where

From 24.11.2015 to 07.01.2016

On the 24.11, 27.11, 28.11, 01.12, 03.12, 04.12, 08.12 and 10.12, the class is from 9:00 to 12:00

On the 29.12, 31.12, 05.01 and 07.01, the class is from 13:30 to 16:30

Place: Room 303 SAIF

### Course Objective

The objective of this course is to introduce the mathematics needed for the

- pricing of financial assets, such as options and other derivatives
- optimal portfolio choice
- modern risk management

Stochastics as a mathematical field developed parallel to the emergence of the finance industry (first insurance, then stock markets, derivatives, etcâ€¦).
This lecture aims at being an introduction to
the mathematics needed in modern finance. We cover the arbitrage theory, pricing of financial assets such as European and American options as well as the optimal portfolio selection.
We also address modern risk management theory such as risk measures and risk allocations which are nowadays of paramount importance in the financial industry.
We illustrate the application of these theories by implementing some classical numerical pricing methods.

We will cover

- Optimization
- Stochastic process (discrete)
- Dynamic programming and simulation
- Stochastic integrals and Ito formula
- Derivatives Pricing
- Change of measure
- American Options Pricing
- Risk measures (Value at Risk, Expected Shortfall, Risk Allocation)

### Literature, Prerequisite and Assessment

Based on lecture notes provided throughout the lecture.
A good knowledge of advanced calculus, linear algebra and basic probability theory is mandatory.
The final grade for the course will be based on a final exam (70%) and 5 homeworks (30%).

[1] H. Follmer and A. Schied, Stochastic Finance. An Introduction in
Discrete Time, de Gruyter Studies in Mathematics, Walter de Gruyter,
Berlin, New York, 2 ed., 2004.