### Lecture

**Optimization Methods in Finance**

### Lecturer

### Assistant

### News

### Description

Many computational problems in finance can be solved by optimization techniques. This course will cover a selection of such methods which are nowadays the basis of many products offered by financial service providers. The students will get to learn the main optimization techniques and will be anabled use them to solve typical optimization problems arizing in finance.

Especially the following topics will be covered.

- Linear Programming: Computing a dedicated bond portfolio, asset pricing
- Quadratic Programming: Portfolio Optimization (Markowitz model)
- Integer Programming: Constructing an index fund
- Dynamic Programming: Option Pricing, Structuring asset backed securities
- Stochastic Programming: Asset/Liability management

The lectures and the exercises will be given in English. We assume basic knowledge in linear algebra and basic programming knowledge in C++ or Matlab.

### Grading

A total amount of 100 “course” points can be reached as follows

- 30 course points from the midterm
- 10 course points from the presentation of a theoretical exercise
- 20 course points for practical exercises
- 40 course points from the final exam

- Exercise 1: 2 practical points
- Exercise 2: 4 practical points
- Exercise 3: 2 practical points
- Exercise 4: 4 practical points
- Exercise 5: 2 practical points
- Bonus project: 4 practical points

A temporary list of reached points, can be found here.

### Schedule

**Lectures**: Wednesday, 14:15-15:45, MA A3 31

(First Lecture: 16.09.09)

**Exercise sessions**: (First Exercise session: 30.09.09)

- Wednesday, 16:00-17:30, MA A3 31
- Thursday, 17:00-18:30, MA A1 10

**Midterm exam**: **November 11, during lecture **

**Final exam**: **January 16, 2010; 8:15h-10:15h in room MA A3 30.** See the following announcement for more details.

### Slides

September, 16

September, 23

September, 30

October, 7

October, 14

October, 21

October, 28

November, 4 (updated writeup for ellipsoid method)

November, 18

November, 25

December, 2

December, 9 (updated)

December, 16

### Exercises

The exercises will take place as follows: For the i-th exercise sheet the students are supposed to solve the assignments in the tutorial in week 2i+1. The solutions will be discussed in week 2i+2.