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Modul
Continuous Time Finance [M-MATH-102860]
Credits
8Recurrence
Jedes SommersemesterDuration
1 SemesterLanguage
Level
4Version
1Responsible
Organisation
- KIT-Fakultät für Mathematik
Part of
Bricks
Identifier | Name | LP |
---|---|---|
T-MATH-105930 | Continuous Time Finance | 8 |
Competence Certificate
oral examination of ca. 30 min.
Competence Goal
Students are able to
- understand, describe and use fundamental notions and techniques of modern continuous time finance,
- use specific probabilistic techniques,
- analyze mathematically economical questions in option pricing and optimization
Prerequisites
The module cannot be completed together with "Stochastic Calculus and Finance [T-WIWI-103129]".
Content
- Stochastic processes and filtrations
- Martingales in continuous time
- Stopping times
- Quadratic variation - Stochastic Ito-Integral w.r.t. continuous semimartingales
- Ito-calculus
- Ito-Doeblin formula
- Stochastic exponentials
- Girsanov theorem
- Martingale representation - Black-Scholes financial market
- Arbitrage and equivalent martingale measures
- Options and no-arbitrage prices
- market completeness - Portfolio optimization
- Bonds, forwards and interest rate models
Recommendation
The content of the module „Probability theory“ is strongly recommended. The module „Discrete time finance“ is recommended.
Workload
Total workload: 240 hours
Attendance: 90 h
- lectures, problem classes and examination
Self studies: 150 h
- follow-up and deepening of the course content,
- work on problem sheets
- literature study and internet research on the course content,
- preparation for the module examination