MAT9750 – Mathematical Finance: Modelling and Risk Management

Schedule, syllabus and examination date

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Course content

MAT9750 gives an introduction to stochastic analysis and calculus for jump processes. The attention is on Levy processes as a flexible class for modelling. The course introduces continuous financial modeling for complete and incomplete markets. We will present techniques needed for risk assessment and management. This includes no-arbitrage theory, pricing of options in complete and incomplete markets. Special attention is paid to the cases of Black-Scholes and exponential Levy models. We will present the hedging problem in both complete and incomplete markets. Special attention is given to the perfect hedging in the Black-Scholes model, in contrast to the imperfect hedging in incomplete markets. We will give an introduction to minimal variance hedging as an example of quadratic hedging. When it comes to risk assessment, the course introduces risk measures, both statically and dynamically.

Learning outcome

After completing the course you will:

  • have an understanding of mathematical modelling in finance, also with aspects towards insurance;
  • have an overview of problems connected to risk evaluation and management in finance;
  • have a knowledge of stochastic methods for jump processes;
  • know how to use techniques in stochastic analysis to financial modelling, pricing of options, hedging and risk measuring.


PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Overlapping courses

* The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 


4 hours of lectures/exercises per week.


mandatory assignment.

Final oral or written examination. The form of examination will be announced by the teaching staff by 15 October/15 March for the autumn semester and the spring semester respectively.

In addition, each PhD candidate will present on a scientific level a short thesis on a chosen topic from the course, selected in collaboration with the lecturer.


Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Explanations and appeals

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.


The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course






Every spring


Every spring

Teaching language