Syllabus

Title
4584 Y1P3 Mathematics II
Instructors
ao.Univ.Prof. Dr. Klaus Pötzelberger
Type
PI
Weekly hours
2
Language of instruction
Englisch
Registration
02/06/19 to 02/24/19
Registration via LPIS
Notes to the course
Subject(s) Master Programs
Dates
Day Date Time Room
Tuesday 03/05/19 01:30 PM - 03:30 PM TC.5.03
Wednesday 03/06/19 09:00 AM - 11:00 AM TC.2.01
Tuesday 03/12/19 01:30 PM - 03:30 PM TC.5.03
Wednesday 03/13/19 09:00 AM - 11:00 AM TC.3.05
Tuesday 03/19/19 01:30 PM - 03:30 PM TC.5.03
Wednesday 03/20/19 09:00 AM - 11:00 AM TC.3.05
Tuesday 03/26/19 01:30 PM - 03:30 PM TC.5.03
Wednesday 03/27/19 02:30 PM - 04:30 PM TC.0.01 ERSTE
Tuesday 04/02/19 01:30 PM - 03:30 PM TC.4.03
Wednesday 04/03/19 09:00 AM - 11:00 AM TC.3.05
Tuesday 04/09/19 01:30 PM - 03:30 PM TC.4.03
Wednesday 04/10/19 09:00 AM - 11:00 AM TC.3.05
Monday 04/29/19 08:00 AM - 10:00 AM TC.0.01 ERSTE

Contents

Stochastic processes in discrete time, martingales, stopping times, arbitrage, random walk, Wiener process, Poisson process, first exit times, American and European options.

Learning outcomes

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.

Attendance requirements

Full attendance is compulsory. This means that students should attend at least 80% of all lectures, at most one lecture can be missed.

Teaching/learning method(s)

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.

Assessment

  • 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!

Prerequisites for participation and waiting lists

Successful completion of Mathematics I and Financial Markets and Instruments.

Readings

1 Author: D. Lamberton and B. Lapeyre (LL)
Title: Introduction to Stochastic Calculus Applied to Finance

Publisher: Chapman & Hall
Edition: 2
Remarks: ISBN 978-1-58488-626-6
Year: 2008
Content relevant for class examination: Yes
Recommendation: Reference literature
2 Author: S. E. Shreve (S1)
Title: Stochastic Calculus for Finance I

Publisher: Springer
Remarks: ISBN 978-0-387-22527-2
Year: 2005
Content relevant for class examination: Yes
Recommendation: Reference literature
3 Author: S. E. Shreve (S2)
Title: Stochastic Calculus for Finance II

Publisher: Springer
Remarks: ISBN 978-0-387-40101-0
Year: 2004
Content relevant for class examination: Yes
Recommendation: Reference literature
4
Title:

Lecture Notes (LN):

http://statmath.wu.ac.at/courses/qfin_math2/


Content relevant for class examination: Yes
Recommendation: Essential reading for all students
Type: Script

Recommended previous knowledge and skills

  • Advanced Business Mathematics (class Mathematics I of the QFin program)
  • Advanced Business Probability theory (class Probability of the QFin program)

Availability of lecturer(s)

klaus.poetzelberger@wu.ac.at

Unit details

Unit Date Contents
1 Week 1: Martingale theory (discrete time). Definition of martingale – examples – stopping times – sub-and supermartingales. Reference: LN chapter 1.
2

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.

3

Week 3: Single period finance. No arbitrage theory – utility maximization – asset pricing – risk neutrality. Reference: SLN chapter 4. Exam 2.

4

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.
Last edited: 2019-03-01



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