0410 Advanced Topics in Continuous Time Finance
Univ.Prof. Dr. Rüdiger Frey
Contact details
Weekly hours
Language of instruction
09/01/23 to 09/25/23
Registration via LPIS
Notes to the course
Day Date Time Room
Wednesday 11/29/23 02:00 PM - 05:00 PM D4.0.019
Monday 12/04/23 02:00 PM - 05:00 PM D1.1.078
Monday 12/11/23 02:00 PM - 05:00 PM D1.1.078
Monday 12/18/23 02:00 PM - 05:00 PM D1.1.078
Monday 01/08/24 02:00 PM - 05:00 PM D1.1.078
Monday 01/15/24 02:00 PM - 05:00 PM D1.1.078
Monday 01/22/24 02:00 PM - 05:00 PM D1.1.074
Thursday 01/25/24 09:00 AM - 12:00 PM D4.0.127
Monday 01/29/24 02:00 PM - 04:00 PM TC.2.03

In this course we will cover the following topics

1. Ito calculus (Ito formula and Ito integral, Ito processes, Feynman Kac formula and applications)
 2. Black Scholes model and option pricing via PDEs (Black Scholes model, pricing by replication Black-Scholes  PDE, risk-neutral pricing via Feynman Kac, properties of option prices, currency options)
 3. Change of measure and Girsanov theory, martingale approach to Black Scholes model
 4. Further mathematical finance (eg. short-rate models  for the term structure and affine models, change of numeraire, multidimensional Black Scholes model
 5. Optimal stopping and applications (eg. Heinkel Zechner or Leland model)
 6. Optimal control and applications (eg Merton model)

Learning outcomes

This course deepens the understanding of continuous-time finance and it covers a number of advanced topics of Continuous Time Finance.

The aim of this course is to:

  • obtain a good  understanding of the main topics, such as stochastic calculus for Brownian motion, financial mathematics in continuous time and the financial applications
  • understand and describe the properties of simple term-structure models, change of numéraire, optimal stopping and basic stochastic control.
  • Study relevant financial applications

After completing this course the student will also:

  • have deepened his/her ability for teamwork
  • be able to formulate essential problems of CTF and propose possible solutions in a precise way (that is in a mathematical language). This skill is different from a purely intuitive understanding of the topics of this course.
Attendance requirements

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

Teaching/learning method(s)

This course is taught as a lecture accompanied by homework assignments (worked out in a team of 3 people and shortly discussed/presented in the lecture). 


Exercises (30%), presentation (20 %) final exam (50%)

Prerequisites for participation and waiting lists

Quantitative Methods for VGSF students or equivalent


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Last edited: 2023-06-02