Stochastic integration 2019-2020 (code 5374STIN8Y) 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, the Doob-Meyer decomposition, construction and properties of the stochastic integral, Itô's formula, (Brownian) martingale representation theorem, Girsanov's theorem, stochastic differential equations and we will briefly explain their relevance for mathematical finance.AimsAt the end of the course, students
PrerequisitesMeasure theory, stochastic processes at the level of the course Measure Theoretic Probability (2010 version)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. These books form the main basis for the lecture notes that we use for the course.Companion courseIn the past students were recommended to take also the course on Stochastic Processes, up to 2018 by Floske Spieksma (UL). The current course of the Dutch Master Program in Mathematics is taught by Daniel Valesin (RuG) and Christian Hirsch (RuG).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up coursesA course that heavily relies on stochastic calculus is Interest rate models (the webpage is a bit outdated, but still fine for a first impression). Another interesting course, more theoretical, is Advanced Topics in Stochastic Analysis.LecturersAsma Khedher (first half) and Peter Spreij (second half), assistance by Sven Karbach.HomeworkCompulsory! Strict deadlines: hand in during 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: Thursdays, 09:00-10:45 in room G3.10 (exception: G5.29 on March 5), first lecture on Thursday 6 February 2020. Tutorials biweekly after the lectures. For up to date information on the lecture rooms, see datanose.nl. See also the map of Science Park and the travel directions. See below for the "corona" adjustments.ExaminationThe final grade is a combination of the results of the take home assignments and the written or oral exam (first part, to be decided) and oral exam (second part). The homework results count for 40% of the final grade. The partial oral exams have equal weight. For the oral exams appointments with the lecturers will be scheduled.What do you have to know? The theory, i.e. all important definitions and results (lemma's, theorems, etc.), but not those in sections that have not been treated. Optional: for each part you may prepare three theorems together with their proofs. You select your favourite 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, after which you will be questioned on different topics. There is a schedule, that will regularly be updated. Warning: sometimes there are problems with synchronizing files on surfdrive, so the file may not always be up to date, or a previous web address (url) has to be replaced with a newer one. 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.Important!Due to the immensely fast spreading corona virus there will no regular lectures from week 8 on. Instead, there will be screen recordings of the lecture notes, together with detailed comments. The recordings will appear on Canvas and should be available every week at the originally scheduled class hours (or earlier). More information will follow. The study programme is as below, in particular valid for the second half.Note that there is no lecture scheduled for April 2, the lecture of week 9 is scheduled for April 9. The programme will be regularly updated! 1st half, old programme
To the Korteweg-de Vries Instituut voor Wiskunde or to the homepage of the master's programme in Stochastics and Financial Mathematics. |