Christoph Czichowsky: Catalogue data in Spring Semester 2020

Name Dr. Christoph Czichowsky
DepartmentMathematics
RelationshipAssociate Examiner

NumberTitleECTSHoursLecturers
401-3888-00LIntroduction to Mathematical Finance Information
A related course is 401-3913-01L Mathematical Foundations for Finance (3V+2U, 4 ECTS credits). Although both courses can be taken independently of each other, only one will be recognised for credits in the Bachelor and Master degree. In other words, it is not allowed to earn credit points with one for the Bachelor and with the other for the Master degree.
10 credits4V + 1UC. Czichowsky
AbstractThis is an introductory course on the mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. We discuss arbitrage, completeness, risk-neutral pricing and utility maximisation. We prove the fundamental theorem of asset pricing and the hedging duality theorems, and also study convex duality in utility maximization.
ObjectiveThis is an introductory course on the mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. We discuss arbitrage, completeness, risk-neutral pricing and utility maximisation, and maybe other topics. We prove the fundamental theorem of asset pricing and the hedging duality theorems in discrete time, and also study convex duality in utility maximization.
ContentThis course focuses on discrete-time financial markets. It presumes a knowledge of measure-theoretic probability theory (as taught e.g. in the course "Probability Theory"). The course is offered every year in the Spring semester.

This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MF II), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MF I, is taken prior to MF II.

For an overview of courses offered in the area of mathematical finance, see https://www.math.ethz.ch/imsf/education/education-in-stochastic-finance/overview-of-courses.html.
Lecture notesThe course is based on different parts from different textbooks as well as on original research literature. Lecture notes will not be available.
LiteratureLiterature:

Michael U. Dothan, "Prices in Financial Markets", Oxford University Press

Hans Föllmer and Alexander Schied, "Stochastic Finance: An Introduction in Discrete Time", de Gruyter

Marek Capinski and Ekkehard Kopp, "Discrete Models of Financial Markets", Cambridge University Press

Robert J. Elliott and P. Ekkehard Kopp, "Mathematics of Financial Markets", Springer
Prerequisites / NoticeA related course is "Mathematical Foundations for Finance" (MFF), 401-3913-01. Although both courses can be taken independently of each other, only one will be given credit points for the Bachelor and the Master degree. In other words, it is also not possible to earn credit points with one for the Bachelor and with the other for the Master degree.

This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MF II), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MF I, is taken prior to MF II.

For an overview of courses offered in the area of mathematical finance, see https://www.math.ethz.ch/imsf/education/education-in-stochastic-finance/overview-of-courses.html.
401-4910-20LSeminar on Mean-Field Games Information
Limited number of participants.
Registration to the seminar will only be effective once confirmed by email from the organiser.
4 credits2SC. Czichowsky
AbstractMean-field games provide a tractable model of large population strategic games. Introduced in the seminal works of Lasry and Lions, and Huang, Malhame and Caines, mean-field games enjoy growing interest by researchers and a wide variety of applications.
In this seminar we want to acquaint ourselves with the basic problem formulation and some approaches to study such games.
ObjectiveStudent should be at a sufficiently advanced level to present selected topics from research papers and books. The seminar will take an intermediate form, somewhere between a student seminar and a graduate reading course. As such, participants should be motivated to prepare a presentation based on research articles, but also willing to consult more senior participants for feedback and help if needed. Roughly the first half of the planned talks is suitable for masters students with a firm understanding of the probabilistic and analytic techniques, the remaining talks will be given by more advanced participants.
ContentThe seminar will begin by recalling classical control theory, known results from stochastic differential games and then quickly progress to research-level topics on mean-field games. Over the course of the seminar we aim to gain a solid overview of current research on this topic. The typical participant will be an advanced graduate student, doctoral student or a postdoc, not necessarily an expert on the topic but interested in jointly learning the subject.
The mean-field games literature employs an interesting mix of techniques form PDEs, stochastic analysis and optimal transport theory. The seminar provides a good staring point for students to write a M.Sc. thesis in this or related areas.
LiteratureThe seminar outline and references are available on the course website:
https://metaphor.ethz.ch/x/2020/fs/401-4910-20L/
Prerequisites / NoticePlease contact Robert (rc@math.ethz.ch) upon registering for the Seminar.

Requirements:
Students are required to meet with an assistant for the seminar twice before their talk. The first meeting is intended to discuss the basic outline and topics covered, the a second meeting to clarify questions and make sure the talk is coherently planed in order to lay the foundations for the following talks.

Prerequisites:
Please consult the seminar website and outline for details.