Coursebooks 2017-2018

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Martingales in financial mathematics

MATH-470

Lecturer(s) :

Schmutz Michael

Language:

English

Summary

The aim of the course is to apply the theory of martingales in the context of mathematical finance. The course provides a detailed study of the mathematical ideas that are used in modern financial mathematics. Moreover, the concepts of complete and incomplete markets are discussed.

Content

- Fundamental results

- Binomial- and trinomial model

- The Snell envelope, optimal stopping, and American options

- Option pricing and hedging

- Exotic options

- Local- and stochastic volatility models

- Stochastic interest rates

- Lévy driven models

- New trends in financial mathematics

Keywords

martingales, financial mathematics, theory of (no-)arbitrage

Learning Prerequisites

Recommended courses

Stochastic calculation

Important concepts to start the course

Stochastic calculation

Learning Outcomes

By the end of the course, the student must be able to:

Assessment methods

Exam oral

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Office hours Yes
Assistants No
Forum No
Others Office hours: Friday, 13:00-14:00

Resources

Virtual desktop infrastructure (VDI)

No

Bibliography

Ressources en bibliothèque

In the programs

  • Applied Mathematics, 2017-2018, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Martingales in financial mathematics
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2017-2018, Master semester 4
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Martingales in financial mathematics
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2017-2018, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Martingales in financial mathematics
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Martingales in financial mathematics
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 4
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Martingales in financial mathematics
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German