Stochastic integration 2015-2016
ContentsStochastic calculus is an indispensable tool in modern financial mathematics. In this course we present this mathematical theory. We treat the following topics from martingale theory and stochastic calculus: martingales in discrete and continuous time, construction and properties of the stochastic integral, Itô's formula, Girsanov's theorem, stochastic differential equations and we will briefly explain their relevance for mathematical finance.
PrerequisitesMeasure theory, stochastic processes at the level of the course Measure Theoretic Probability
LiteratureRecommended background reading: I. Karatzas and S.E. Shreve, Brownian motions and stochastic calculus and D. Revuz and M. Yor, Continuous martingales and Brownian motion. The contents of the course are described in the (based on these books) lecture notes.
Companion courseStudents are recommended to take also the course on Stochastic Processes, see the Spring Courses of the Dutch Master Program in Mathematics.
Follow up coursesA course that heavily relies on stochastic calculus is Interest rate models (the webpage is a bit outdated, but still fine for a first impression).
LecturersSonja Cox (part II) and Peter Spreij (part I), assisted by Nicos Starreveld
HomeworkStrict deadlines: the lecture after you have been given the assignment, although serious excuses will always be accepted. You are allowed to work in pairs (a pair means 2 persons, not 3 or more), in which case one set of solutions should be handed in.
ScheduleSpring semester: First lecture on Thursday 4 February 2016, 13:00-15:00. Lectures until 17 March in G2.04 (Science Park), from March 31 on in G0.10 but see also datanose.nl for up to date information. See the map of Science Park and the travel directions (in Dutch only). No lecture on March 3, March 24, May 5th and May 26. There is a lecture on April 28!.
ExaminationThe final grade is a combination of the results of the take home assignments and the oral exam (first part) and written exam (second part). To take the oral exam, you make an appointment for a date that suits your own agenda. If it happens that you'd like to postpone the appointment, just inform us that you want so. This is never a problem! The only important matter is that you take the exam, when you feel ready for it. What do you have to know? The theory, i.e. all important definitions and results (lemma's, theorems, etc.). Optional: you may prepare three theorems together with their proofs. You select your favorite ones! Criteria to consider: they should be interesting, non-trivial and explainable in a reasonably short time span. You will be asked to present one of them. Unavailable periods will appear here.
RegistrationThe UvA now wants all participants to be registered four weeks before the start of the course. If you missed this deadline you can use the late registration form. Note that a UvAnetID is required, so at least you have to be registered as a UvA student.
(regularly updated, Last modified: 01 April 2016 13:59)
To the Korteweg-de Vries Instituut voor Wiskunde or to the homepage of the master's programme in Stochastics and Financial Mathematics.