Stochastic integration 2011-2012 (code ST409018) ContentsStochastic calculus is an indispensable tool in modern financial mathematics. In this course we present this mathematical theory and apply it to the problem of pricing and hedging of financial derivatives. 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. As an application, we explain how stochastic differential equations are typically used to model financial markets and we discuss the problem of the pricing of derivatives such as stock options.PrerequisitesMeasure theory, stochastic processes at the level of the course Measure Theoretic ProbabilityLiteratureRecommended 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 lecture notes (which are based on these books, updated version composed during this spring).
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 coursesCourses that heavily rely on stochastic calculus are Financial Stochastics and Control of Stochastic Systems in Continuous Time.LecturersPeter Spreij, assisted by Naser Asghari.HomeworkStrict deadlines: the lecture after you have been given the assignment, although serious excuses will always be accepted.ScheduleSpring semester: Thursdays, 11:00-13:00, Room B0.209 (Science Park); see the map of Science Park and the travel directions. First lecture on 9 February 2012 (starting at 10:00), March 1 class: 09:00-11:00 taught by Neil Walton, no class on March 29.ExaminationThe final grade is a combination of the results of the take home assignments and the oral exam. 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. I'll then ask you to present two of them. I am unavailable in the periods 17-22 May, 6-14 June, 29 June - 4 July and more....Programme(last modified: )
To the Korteweg-de Vries Instituut voor Wiskunde or to the homepage of the master's programme in Stochastics and Financial Mathematics. |