Modul

The module will be completed with an oral exam (approx. 30 min).

The students will

• know fundamental examples for linear and non-linear stochastic differential equations,
• be able to apply basic solution concepts for stochastic differential equations,
• know fundamental theorems of stochastic calculus and will be able to apply these to stochastic differential equations.

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1. Introduction and recapitulation of stochastic integration, Itô's formula, Lévy Theorem
2. Burkholder-Davis-Gundy inequality
3. Existence and uniqueness of solutions of stochastic differential equations
4. Explicit solutions of linear stochastic differential equations
5. Change of the time scale of Brownian motion
6. Representation of continuous time martingales
7. Brownian martingales
8. Local and global solutions of stochastic differential equations
9. Girsanov Theorem

The contents of the course "Probability Theory" are strongly recommended. The contents of the course "Continuous Time Finance" are recommended.

Total workload: 120 hours

Attendance: 45 hours

• lectures, problem classes, and examination 

Self-studies: 75 hours

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research relating to the course content,
• preparation for the module examination