MAT9740 - Malliavin Calculus and Applications to Finance

Schedule, syllabus and examination date

Choose semester

Course content

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.

Learning outcome

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.

Admission

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.

Prerequisites

Formal prerequisite knowledge

None

Recommended previous knowledge

Overlapping courses

10 credits overlap with MAT4740 - Malliavin Calculus and Applications to Finance

* For information about the potential partial overlap with other courses, contact the Department.

Teaching

4 hours per week, including exercises.

Examination

Oral exam

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.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Evaluation

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

Credits

10

Level

PhD

Teaching

Spring 2018

Spring 2014

Spring 2013

Spring 2010

Spring 2008

Spring. Taught according to demand and resources. If you want to attend the course, please send an e-mail to studieinfo@math.uio.no.

Examination

Spring 2018

Spring 2014

Spring 2013

Spring 2010

Spring 2008

Spring. According to demand and resources.

Teaching language

English

The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.