Syllabus

Titel
4584 Y1P3 Mathematics II
LV-Leiter/innen
ao.Univ.Prof. Dr. Klaus Pötzelberger
Kontakt
  • LV-Typ
    PI
  • Semesterstunden
    2
  • Unterrichtssprache
    Englisch
Anmeldung
06.02.2019 bis 24.02.2019
Anmeldung über LPIS
Hinweise zur LV
Planpunkt(e) Master
Termine
Wochentag Datum Uhrzeit Raum
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

Inhalte der LV

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

Lernergebnisse (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.

Regelung zur Anwesenheit

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

Lehr-/Lerndesign

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.

Leistung(en) für eine Beurteilung

  • 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!

Teilnahmevoraussetzung(en) und Vergabe von Wartelistenplätzen

Successful completion of Mathematics I and Financial Markets and Instruments.

Literatur

1 Autor/in: D. Lamberton and B. Lapeyre (LL)
Titel: Introduction to Stochastic Calculus Applied to Finance

Verlag: Chapman & Hall
Auflage: 2
Anmerkungen: ISBN 978-1-58488-626-6
Jahr: 2008
Prüfungsstoff: Ja
Empfehlung: Referenzliteratur
2 Autor/in: S. E. Shreve (S1)
Titel: Stochastic Calculus for Finance I

Verlag: Springer
Anmerkungen: ISBN 978-0-387-22527-2
Jahr: 2005
Prüfungsstoff: Ja
Empfehlung: Referenzliteratur
3 Autor/in: S. E. Shreve (S2)
Titel: Stochastic Calculus for Finance II

Verlag: Springer
Anmerkungen: ISBN 978-0-387-40101-0
Jahr: 2004
Prüfungsstoff: Ja
Empfehlung: Referenzliteratur
4
Titel:

Lecture Notes (LN):

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


Prüfungsstoff: Ja
Empfehlung: Unbedingt notwendige Studienliteratur für alle Studierenden
Art: Skriptum

Empfohlene inhaltliche Vorkenntnisse

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

Erreichbarkeit des/der Vortragenden

klaus.poetzelberger@wu.ac.at

Detailinformationen zu einzelnen Lehrveranstaltungseinheiten

Einheit Datum Inhalte
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.
Zuletzt bearbeitet: 01.03.2019



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