|Dienstag||05.03.2019||13:30 - 15:30||TC.5.03|
|Mittwoch||06.03.2019||09:00 - 11:00||TC.2.01|
|Dienstag||12.03.2019||13:30 - 15:30||TC.5.03|
|Mittwoch||13.03.2019||09:00 - 11:00||TC.3.05|
|Dienstag||19.03.2019||13:30 - 15:30||TC.5.03|
|Mittwoch||20.03.2019||09:00 - 11:00||TC.3.05|
|Dienstag||26.03.2019||13:30 - 15:30||TC.5.03|
|Mittwoch||27.03.2019||14:30 - 16:30||TC.0.01 ERSTE|
|Dienstag||02.04.2019||13:30 - 15:30||TC.4.03|
|Mittwoch||03.04.2019||09:00 - 11:00||TC.3.05|
|Dienstag||09.04.2019||13:30 - 15:30||TC.4.03|
|Mittwoch||10.04.2019||09:00 - 11:00||TC.3.05|
|Montag||29.04.2019||08:00 - 10:00||TC.0.01 ERSTE|
After completing this course the student will have the ability to:
- describe the basic concepts and definitions of stochastic processes in discrete time, martingales, stopping times, arbitrage, random walk, Wiener process, Poisson process, first exit times.
- work with the basic concepts and definitions of stochastic processes in discrete time, martingales, stopping times, arbitrage, random walk, Wiener process, Poisson process, first exit times.
After completing this course the student will also have the ability to:
- confidently organize and integrate mathematical ideas and information.
- shift mathematical material quickly and efficiently, and to structure it into a coherent mathematical argument.After completing this course the student will also have the ability to:
- solve applied problems where skills are required from the theory of stochastic processes.
Full attendance is compulsory. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.
The class is taught as a lecture accompanied with homework assignments. The lectures are aimed at providing the theoretical framework, while weekly exams check the study progress.
Course Reading: The contents of the class are covered by the references listed on learn@wu in the corresponding section.
- 30% written weekly exams
- 30% midterm exam
- 40% endterm exam
For the written final exam, the midterm exam and the weekly exams, the assessment will be based on the ability to describe and apply the key concepts discussed throughout the course and to choose the appropriate analytical techniques to obtain the relevant information. The weekly exams and the endterm exam cannot be retaken. Students need to get at least 50% of the possible points to pass this course. All exams are closed-book exams!
Successful completion of Mathematics I and Financial Markets and Instruments.
- Advanced Business Mathematics (class Mathematics I of the QFin program)
- Advanced Business Probability theory (class Probability of the QFin program)
|1||Week 1: Martingale theory (discrete time). Definition of martingale – examples – stopping times – sub-and supermartingales. Reference: LN chapter 1.
Week 2: Applications to gambling. Ruin problem - optional sampling - Wald’s equation – exit probabilities – reflection principle. Equivalent measures. Reference: LN chapter 2+3. Exam 1.
Week 3: Single period finance. No arbitrage theory – utility maximization – asset pricing – risk neutrality. Reference: SLN chapter 4. Exam 2.
Week 4: Multi period finance. Self-financing trading – no-arbitrage theory – martingale measures – binomial trees – asset pricing. Reference: LN chapter 4. Midterm Exam.
|5||Week 5: American options. Optimal strategy – Snell envelope – Doob decomposition. Reference: LNchapter 5. Exam 3.
|6||Week 6: Wiener process. Definition and properties of Wiener process – reflection principle – first exit times. Reference: LN chapter 6. Exam 4.
|7||Week 7: Final Exam.|