MAT9740 - Malliavin Calculus and Applications to Finance
The course gives an introduction to Malliavin calculus for Lévy processes and its applications to mathematical finance. The theoretical part will first deal with Malliavin calculus for Brownian motion and then with Malliavin calculus for pure jump Lévy processes. Corresponding to each of these two cases, the following topics will be covered: Chaos expansions, Malliavin derivatives, Skorohod integrals, forward integrals, Wick products and anticipative stochastic calculus. The applications to finance include the following topics: The Clark-Ocone formula and explicit hedging expressions in complete markets, efficient numerical methods for the computations of the "greeks" in finance, explicit minimal variance hedging formulas in incomplete markets, insider trading.
The purpose of the course is to give a presentation of the current state-of-the-art of the theory and applications of Malliavin calculus, in some cases leading to the research frontier within this area of stochastic calculus and mathematical finance. It is intended for Ph.D. students, postdocs and other researchers/practitioners in this field.
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.
Formal prerequisite knowledge
Recommended previous knowledge
10 credits overlap with MAT4740 - Malliavin Calculus and Applications to Finance
* For information about the potential partial overlap with other courses, contact the Department.
4 hours per week, including exercises.
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.
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.
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.