Syllabus

Title
4432 Y1P3 Mathematics II
Instructors
ao.Univ.Prof. Dr. Klaus Pötzelberger
Type
PI
Weekly hours
2
Language of instruction
Englisch
Registration
01/31/22 to 02/18/22
Registration via LPIS
Notes to the course
Subject(s) Master Programs
Dates
Day Date Time Room
Tuesday 03/01/22 01:30 PM - 03:30 PM TC.3.01
Wednesday 03/02/22 01:30 PM - 03:30 PM TC.5.15
Tuesday 03/08/22 01:30 PM - 03:30 PM TC.3.01
Wednesday 03/09/22 01:30 PM - 03:30 PM TC.5.15
Tuesday 03/15/22 01:30 PM - 03:30 PM TC.3.01
Wednesday 03/16/22 09:00 AM - 11:00 AM TC.5.15
Tuesday 03/22/22 01:30 PM - 03:30 PM TC.3.01
Wednesday 03/23/22 09:00 AM - 11:00 AM TC.5.15
Tuesday 03/29/22 01:30 PM - 03:30 PM TC.3.01
Wednesday 03/30/22 09:00 AM - 11:00 AM D5.0.001
Tuesday 04/05/22 01:30 PM - 03:30 PM TC.3.01
Wednesday 04/06/22 09:00 AM - 11:00 AM TC.5.15
Wednesday 04/20/22 09:00 AM - 11:00 AM D5.0.001
Contents

Stochastic processes in discrete time, martingales, stopping times, arbitrage, random walk, Wiener 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, first exit times.
  • work with the basic concepts and definitions of stochastic processes in discrete time, martingales, stopping times, arbitrage, random walk, Wiener 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 have attend at least 80% of all lectures.

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.

If decreed, the course is taught as an online course.

Course Reading: The contents of the class are covered by the references listed on learn@wu in the corresponding section.

 

Assessment
  • 30% homework exercises
  • 30% midterm exam
  • 40% endterm exam

For the written final exam, the midterm exam and the weekly homework exercises, 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 exams  cannot be retaken. Students need to get at least 50% of the possible points to pass this course.

Whether the exams are online or with physical presence, depends on the situtation regarding the COVID pandemic.

 

 

Readings

Please log in with your WU account to use all functionalities of read!t. For off-campus access to our licensed electronic resources, remember to activate your VPN connection connection. In case you encounter any technical problems or have questions regarding read!t, please feel free to contact the library at readinglists@wu.ac.at.

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.

3

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

4

Week 4: Multi period finance. Self-financing trading – no-arbitrage theory – martingale measures – binomial trees – asset pricing. Reference: LN chapter  4.

5

Week 5: American options. Optimal strategy – Snell envelope – Doob decomposition. Reference:  LN chapter 5. Midterm Exam.

6

Week 6: Wiener process. Definition and properties of Wiener process – reflection principle – first exit times. Reference: LN chapter 6.

7 Week 7: Final Exam.
Last edited: 2022-05-02



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