1909 Stochastic Processes with Jumps and Applications in Finance and Economics
Univ.Prof. Dr. Rüdiger Frey
Contact details
Weekly hours
Language of instruction
09/18/23 to 10/06/23
Registration via LPIS
Notes to the course
Day Date Time Room
Thursday 11/09/23 09:00 AM - 12:00 PM D4.0.047
Thursday 11/16/23 09:00 AM - 12:00 PM D2.0.330
Thursday 11/23/23 09:00 AM - 12:00 PM D4.0.047
Thursday 11/30/23 09:00 AM - 12:00 PM D4.0.047
Thursday 12/07/23 09:00 AM - 12:00 PM D4.0.047
Thursday 12/14/23 09:00 AM - 12:00 PM D4.0.047
Thursday 12/21/23 09:00 AM - 12:00 PM D4.0.047
Thursday 01/11/24 09:00 AM - 12:00 PM D4.0.047
Thursday 01/18/24 09:00 AM - 12:00 PM D4.0.047

Asset price processes with jumps have been advocated as a tool to overcome some of the empirical deficiencies of models based on Brownian motion such as the Black Scholes model.

This lecture gives an introduction to the theory of stochastic processes with jumps with a view towards applications in finance. We will cover basic jump processes, Levy processes and their mathematical construction and elements of stochastic calculus for jump processes. Armed with these results we will study the pricing and the hedging of derivatives in financial models with jumps using probabilistic methods and partial integro-differential equations.

Learning outcomes

This course deepens the understanding of continuous-time finance by extending known results to processes with  jumps. This is indispensable for understanding  a large part of the current research in financial mathematics.

The aim of this course is to:

  • obtain a thorough understanding of the main topics, such as Levy processes or stochastic calculus for general semimartingales and random measures
  • enable the sudents to understand and contribute to  current research in financial mathematics

After completing this course the student will also:

  • have deepened his/her ability for teamwork
  • have deepened his/her presentation skills
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)

The first part of the course (approx 6 units) consist of lectures of the instructor. This is followed by student presentations where various applications of jump processes in financial mathematics are discussed.


Presentation during the course 30%, final exam 60%, active class participationm 10%.


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Recommended previous knowledge and skills

Lectures Continuous Time Finance I and II from the MSc Qfin or equivalent. In case of doubt please contact the instructor.

Availability of lecturer(s)

Last edited: 2023-11-08