Josef Teichmann: Katalogdaten im Herbstsemester 2021

NameHerr Prof. Dr. Josef Teichmann
LehrgebietFinanzmathematik
Adresse
Professur für Finanzmathematik
ETH Zürich, HG G 54.2
Rämistrasse 101
8092 Zürich
SWITZERLAND
Telefon+41 44 632 31 74
E-Mailjosef.teichmann@math.ethz.ch
URLhttp://www.math.ethz.ch/~jteichma
DepartementMathematik
BeziehungOrdentlicher Professor

NummerTitelECTSUmfangDozierende
364-1058-00LRisk Center Seminar Series0 KP2SB. J. Bergmann, D. Basin, A. Bommier, D. N. Bresch, L.‑E. Cederman, P. Cheridito, F. Corman, O. Fink, H. Gersbach, C. Hölscher, K. Paterson, H. Schernberg, F. Schweitzer, D. Sornette, B. Stojadinovic, B. Sudret, J. Teichmann, U. A. Weidmann, S. Wiemer, M. Zeilinger, R. Zenklusen
KurzbeschreibungThis course is a mixture between a seminar primarily for PhD and postdoc students and a colloquium involving invited speakers. It consists of presentations and subsequent discussions in the area of modeling complex socio-economic systems and crises. Students and other guests are welcome.
LernzielParticipants should learn to get an overview of the state of the art in the field, to present it in a well understandable way to an interdisciplinary scientific audience, to develop novel mathematical models for open problems, to analyze them with computers, and to defend their results in response to critical questions. In essence, participants should improve their scientific skills and learn to work scientifically on an internationally competitive level.
InhaltThis course is a mixture between a seminar primarily for PhD and postdoc students and a colloquium involving invited speakers. It consists of presentations and subsequent discussions in the area of modeling complex socio-economic systems and crises. For details of the program see the webpage of the colloquium. Students and other guests are welcome.
SkriptThere is no script, but a short protocol of the sessions will be sent to all participants who have participated in a particular session. Transparencies of the presentations may be put on the course webpage.
LiteraturLiterature will be provided by the speakers in their respective presentations.
Voraussetzungen / BesonderesParticipants should have relatively good mathematical skills and some experience of how scientific work is performed.
401-3461-00LFunctional Analysis I
Höchstens eines der drei Bachelor-Kernfächer
401-3461-00L Funktionalanalysis I / Functional Analysis I
401-3531-00L Differentialgeometrie I / Differential Geometry I
401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory
ist im Master-Studiengang Mathematik anrechenbar. Die Kategoriezuordnung können Sie in diesem Fall nicht selber in myStudies vornehmen, sondern Sie müssen sich dazu nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (www.math.ethz.ch/studiensekretariat) wenden.
10 KP4V + 1UJ. Teichmann
KurzbeschreibungBaire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces.
LernzielAcquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps.
LiteraturRecommended references include the following:

Michael Struwe: "Funktionalanalysis I" (Skript available at https://people.math.ethz.ch/~struwe/Skripten/FA-I-2019.pdf)

Haim Brezis: "Functional analysis, Sobolev spaces and partial differential equations". Springer, 2011.

Peter D. Lax: "Functional analysis". Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Elias M. Stein and Rami Shakarchi: "Functional analysis" (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Manfred Einsiedler and Thomas Ward: "Functional Analysis, Spectral Theory, and Applications", Graduate Text in Mathematics 276. Springer, 2017.

Walter Rudin: "Functional analysis". International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.
Voraussetzungen / BesonderesSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with topology and measure theory, in part. Lebesgue integration and L^p spaces).
401-5820-00LSeminar in Computational Finance for CSE4 KP2SJ. Teichmann
Kurzbeschreibung
Lernziel
InhaltWe aim to comprehend recent and exciting research on the nature of
stochastic volatility: an extensive econometric research [4] lead to new in-
sights on stochastic volatility, in particular that very rough fractional pro-
cesses of Hurst index about 0.1 actually provide very attractive models. Also
from the point of view of pricing [1] and microfoundations [2] these models
are very convincing.
More precisely each student is expected to work on one specified task
consisting of a theoretical part and an implementation with financial data,
whose results should be presented in a 45 minutes presentation.
Literatur[1] C. Bayer, P. Friz, and J. Gatheral. Pricing under rough volatility.
Quantitative Finance , 16(6):887-904, 2016.

[2] F. M. Euch, Omar El and M. Rosenbaum. The microstructural founda-
tions of leverage effect and rough volatility. arXiv:1609.05177 , 2016.

[3] O. E. Euch and M. Rosenbaum. The characteristic function of rough
Heston models. arXiv:1609.02108 , 2016.

[4] J. Gatheral, T. Jaisson, and M. Rosenbaum. Volatility is rough.
arXiv:1410.3394 , 2014.
Voraussetzungen / BesonderesRequirements: sound understanding of stochastic concepts and of con-
cepts of mathematical Finance, ability to implement econometric or simula-
tion routines in MATLAB.
401-5910-00LTalks in Financial and Insurance Mathematics Information 0 KP1KB. Acciaio, P. Cheridito, D. Possamaï, M. Schweizer, J. Teichmann, M. V. Wüthrich
KurzbeschreibungResearch colloquium
Lernziel
InhaltRegular research talks on various topics in mathematical finance and actuarial mathematics
406-2604-AALProbability and Statistics
Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben.

Alle anderen Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen.
7 KP15RJ. Teichmann
KurzbeschreibungIntroduction to probability and statistics with many examples, based on chapters from the books "Probability and Random Processes" by G. Grimmett and D. Stirzaker and "Mathematical Statistics and Data Analysis" by J. Rice.
LernzielThe goal of this course is to provide an introduction to the basic ideas and concepts from probability theory and mathematical statistics. In addition to a mathematically rigorous treatment, also an intuitive understanding and familiarity with the ideas behind the definitions are emphasized. Measure theory is not used systematically, but it should become clear why and where measure theory is needed.
InhaltProbability:
Chapters 1-5 (Probabilities and events, Discrete and continuous random variables, Generating functions) and Sections 7.1-7.5 (Convergence of random variables) from the book "Probability and Random Processes". Most of this material is also covered in Chap. 1-5 of "Mathematical Statistics and Data Analysis", on a slightly easier level.

Statistics:
Sections 8.1 - 8.5 (Estimation of parameters), 9.1 - 9.4 (Testing Hypotheses), 11.1 - 11.3 (Comparing two samples) from "Mathematical Statistics and Data Analysis".
LiteraturGeoffrey Grimmett and David Stirzaker, Probability and Random Processes.
3rd Edition. Oxford University Press, 2001.

John A. Rice, Mathematical Statistics and Data Analysis, 3rd edition.
Duxbury Press, 2006.