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MAT4740 - Malliavin Calculus and Applications to Finance

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 outcomes

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

Students at UiO must apply for courses in StudentWeb.

International applicants, if you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

The examination in this course is not available for external candidates. Only students admitted to the course may sit for the examination.

Prerequisites

Recommended prior knowledge

MAT4710 - Stochastic analysis II

Teaching

4 hours per week, including exercises, in the spring semester.

Exam information

Oral exam

Exam resources

No special exam resources are allowed.

Assessment and grading

Course grades are awarded on a descending scale using alphabetic grades from A to E for passes and F for fail. Read more about the grading system .

Explanations and appeals

Students can request an explanation of their grades, and can also appeal against their grades or make a complaint about formal examination errors. Read more about explanations and appeals

Possibility of make-up exams and re-takes

Students who due to illness or other valid reason of absence were unable to sit for their final exams may apply for participation in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question. Documentation of valid reasons for absence from the regular exam must be submitted upon application to participate in deferred examinations.

Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.

Information about deferred and new examination (also called repeat examination) is found here

More information about examination at the Faculty of Mathematics and Natural Sciences can be found here

Exam options for students with special needs

Students may apply for access to alternative exam resources or exam forms on the basis of chronic illness and/or special needs that create a marked disadvantage to other students in the exam situation. Mothers who are breastfeeding may apply for extra time to complete the exam.

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