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Contents 1 Course Title 2 Course Code 3 Credit 4 Prerequisites 5 Content 6 Aims 7 Learning Outcomes 8 Suggested Textbooks 9 Outline 10 Resources 11 First Meeting

Course Title

Special Topics: Portfolio Optimization

Course Code

IAM 748

Credit

(3-0)3

Prerequisites

Consent of instructors; basic knowledge in numerical optimization, probability theory, stochastic calculus and in the financial sector are helpful

Content

Coursework and computer lab with MATLAB

Aims

The objective of this course is to introduce central elements of theory, methods (algorithms) and applications on how optimization theory is used to decide about an optimal portfolio.

Learning Outcomes

At the end of this course, students should be able to approximately model, analyze and tackle optimization problems of the financial sector related with portfolios. This includes a macro-economical understanding, a representation of individual interests, and a familiarity with modern mathematical methods. Both lectures and exercises serve for this aim of learning, deepening, applying and preparing.

Suggested Textbooks

• R. Korn and E. Korn, Option Pricing and Portfolio Optimization - Modern methods of financial mathematics, AMS, 2001.
• H. Kraft, Financial Mathematics I: Stochastic Analysis, Option Pricing, Portfolio Optimization, lecture notes, University of Kaiserslautern, Department of Mathematics, Summer Term 2005.
• J.C. Hull, Options, Futures and Other Derivatives, Prentice Hull, 2007.

During the course, further lecture notes, papers and presentations will be handed out to the students.

Outline

• 1.week: Mean-variance approach in a one-period model
• 2.week: Continuous-time market model
• 3.week: Continuous-time market model
• 4.week: Option Pricing
• 5.week: Option Pricing
• 6.week: Pricing of exotic options and numerical algorithms
• 7.week: Pricing of exotic options and numerical algorithms
• 8.week: Introduction and formulation of optimal portfolios
• 9.week: Introduction and formulation of optimal portfolios
• 10.week: Martingale method
• 11.week: Optimal option portfolios
• 12.week: Stochastic control
• 13.week: Portfolio optimization via the stochastic control method
• 14.week: Conclusion and outlook

Resources

• MATLAB 6.1

First Meeting

First Meeting (and Lecture / Exercise)

Thursday, February 19, 9.40-12.30 IAM Building (S-209)