### Objectives

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.

### Topics

- 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

### Schedule

Tuesday 16:15-19:15 (2h Lecture, 1h Exercise)

Last Lecture: December 16

**Room Change: Starting from November 4, lecture and exercise are in room CE 1 101**

### Prerequisites

- Linear Algebra

- Basic Probability

- Some experience with algorithms and coding (no particular programming language)

### Software

During this course a small number of real-world problems has to be modeled and solved with software tools. The students solutions have to be presented in a seminar.

You can find a description how to install ZIMPL and QSOpt here: Installation Guide

The practical exercises can be done in groups up to 3 students. Each group is asked to shortly present their outcome with 2-3 slides in front of the auditory.

October 7: Presentation of exercise 1.6

### Textbook

Textbook

Assignments

Exercise sheet 2

Exercise sheet 3

Exercise sheet 4 Solution

Exercise sheet 5

Exercise sheet 6

September 30: Question on sheet 1

October 7: Discussion of sheet 1

October 14: Question on sheet 2

October 21: Discussion of sheet 2

October 28: Question on sheet 3

November 4: Discussion of sheet 3

November 11: Question on sheet 4

November 18: Discussion of sheet 4

December 2: Question on sheet 5

December 9: Presentation of CVar minimization

December 16: Discussion of sheet 6

Additional Material

You can find Dow Jones index together with all components on a daily or monthly base (1st column is date, 2nd is Dow Jones index, then prices of contained assets follow).

Covered Topics / Slides

September 23 (updated)

September 30: Simplex working example, Markowitz Model

October 7

October 14

October 21

October 28 (updated, 2nd ed.)

November 4

November 11: Midterm. See also the Announcement

November 18

November 25

December 2

December 9 Additional Material: Chapter 5 in Algorithmic Game Theory (see also here)

December 16

Grading

Lecturer

Assistant