Modul

oral examination of ca. 30 min.

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

The module cannot be completed together with "Stochastic Calculus and Finance [T-WIWI-103129]".

• 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

The content of the module „Probability theory“ is strongly recommended. The module „Discrete time finance“ is recommended.

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