Contents |
Course Code
IAM 751 (9700751)
Credit
(3-0) 3
Prerequisites
Good knowledge in numerical optimization, probability theory, stochastic calculus and in the financial sector is necessary; a willingness to work scientifically, self-responsible but also in a team, will be necessary.
Content/Aim
Lectures on advanced methods in financial mathematics given by the instructor; a few talks by guest scientists will be integrated into the schedule; at the end of the semester, the participants will give well-prepared lectures on the outcomes of their challenging term projects. The course content covers and offers:
• Additive and Generalized Additive Models in Finance,
• Advanced Corporate Finance,
• Application of Monte Carlo Methods in Finance,
• Applications of the Root Solution of the Skorohod Embedding Problem,
• Asset Liability Management,
• Behavioral Finance, Racetrack Betting and Options and Futures Trading,
• Change of Time Method in Mathematical Finance,
• Construction of Martingales under Constraints,
• Discrete Stochastic Processes,
• Derivative Prices and Market Behavior,
• Derivatives and Contingent Claim Theory,
• Financial Engineering in Manufacturing Enterprise Systems,
• Financial Markets with Stochastic Volatilities,
• Frontiers of the Rationality - Hypothesis in Finance Theory,
• Grid Computing in Finance,
• Hidden Markov Models in Finance, e.g., in Loan Banking and Life Insurance,
• Investment Strategy for Optimal Capital Growth,
• Managing Guarantee Risk,
• Martingale Measures for NIG Lévy Processes,
• Mathematical Aspects of Financial Physics, e.g., in Risk Management,
• Numerical Methods for Stochastic Differential Equations,
• Numerical Methods for the Markov Functional Model,
• MARS in Finance,
• Multi-Level Optimization: Portfolio Optimization and Parameter Estimation,
• Optimal Control of Stochastic Hybrid Systems,
• Pricing and Hedging Derivatives,
• Robust Optimization in Finance,
• Statistical Arbitrage,
• Stochastic Programming Models, Algorithms and Applications,
• Testing for National Capital Market Efficiency.
The course’s aims consist in a deepened knowledge by the students, and that they are enabled and activated to a do their own scientific work in future. Therefore, the objective of this course is to guide students in their first steps as young researchers on modern areas of mathematical finance. For this purpose, course material will be presented and distributed whose understanding will demand a joint view and application of the different mathematical foundations of finance. This necessitates further reading and deep reflection by all participants, a spirit of scientific entrepreneurship and willingness to become more mature. Approaches and results of the sources taught and distributed will become improved by the participants, and every participant will prepare a small paper on his/her findings that will be submitted.
Learning Outcomes
At the end of this course, students should be able to approach contemporary research areas as young scientists. For this purpose, mathematical knowledge and methodology in finance will be deepened and trained. This will better prepare the participants for their MSc and, in particular, PhD thesis works and their first publications, at an advanced level of maturity. Indeed, a paper will be written by every student. How to write a paper and how to didactically prepare and give an excellent lecture, belongs to the learning outcomes, too.
Suggested Books
At the beginning and throughout the course, various scientific documents will be handed out to the participants: general ones for all participants as well as specific ones according to the individual term and paper project. By visiting libraries, the internet and by contacting further international experts, the students will obtain additional sources and chances to discuss their questions and own scientific ideas. It is planned that two of the chapters of the celebrated PhD thesis of Dr. Daniel Akume, visiting scientist at IAM, will be prepared as sections of a manuscript, distributed and integrated into the schedule of lectures.
Resources
- MATLAB 6.1
Outline
- 1.week: Advanced Theoretical Aspects of Stochastic Differential Equations,
- 2.week: Discrete, Continuous and Lévy Processes in Finance,
- 3.week: Advanced Risk Management in Finance,
- 4.week: Advanced Portfolio Optimization,
- 5.week: Behavioral Finance, Betting, Options and Futures Trading,
- 6.week: Special Aspects of Martingales,
- 7.week: Advanced Statistical Methods in Finance,
- 8.week: Selected Advanced Numerical Methods in Finance,
- 9.week: Optimal Control of Stochastic Hybrid Systems in Finance,
- 10.week: Mathematical Methods for Testing Turkish Capital Market,
- 11.week: Lectures by/with Students,
- 12.week: Lectures by/with Students,
- 13.week: Lectures by/with Students,
- 14.week: Lectures by/with Students, Conclusion and Outlook.