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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.
Students who are admitted to study programmes or individual courses at UiO must each semester register which courses and exams they wish to sign up for by registering a study plan 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.
Only students admitted to the course may take part in instruction and tuition and sit for the examination.
None
MAT4710 - Stochastic analysis II
4 hours per week, including exercises, in the spring semester.
Teaching takes place throughout the semester.
A student who has completed compulsory instruction and coursework and has had these approved, is not entitled to repeat that instruction and coursework. A student who has been admitted to a course, but who has not completed compulsory instruction and coursework or had these approved, is entitled to repeat that instruction and coursework, contingent on available capacity.
Oral exam
No special exam resources are allowed.
Course grades are awarded on a descending scale using alphabetic grades from A to E for passes and F for fail.
A student may appeal against an awarded grade and/or file a formal complaint about exam procedures.
Students who due to illness or other valid reason of absence were unable to sit for their final exams may apply for participation in make-up exams. Make-up exams 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 make-up exams.
Students who have failed an exam and students who wish to re-take an exam to achieve a better grade may not participate in make-up exams, but must re-take the exam when it is regularly scheduled.
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.
Visiting address:
Niels Henrik Abel's building, Moltke Moes vei
Postal address:
P.O.box 1053, Blindern
NO-0316 Oslo
Visiting hours:
Monday-friday 09:00-14:30
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