Josef Teichmann: Catalogue data in Spring Semester 2018 |
| Name | Prof. Dr. Josef Teichmann |
| Field | Financial Mathematics |
| Address | Professur für Finanzmathematik ETH Zürich, HG G 54.2 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 79 584 55 40 |
| josef.teichmann@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~jteichma |
| Department | Mathematics |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-2604-00L | Probability and Statistics | 7 credits | 4V + 2U | J. Teichmann | |
| Abstract | - Laplace models, random walks, conditional probabilities, independence. - Kolmogorov's axioms, random variables, moments, multivariate distributions, laws of large numbers and central limit theorem. - Point estimators, tests and confidence intervals. | ||||
| Learning objective | The goal of this course is to provide an introduction to the basic ideas and concepts from probability theory and mathematical statistics. This includes a mathematically rigorous treatment as well as intuition and getting acquainted with the ideas behind the definitions. The course does not use measure theory systematically, but it does point out where this is required and what the connections are. | ||||
| Content | - Diskrete Wahrscheinlichkeitsräume: Laplace-Modelle, Binomial- und Poissonverteilung, bedingte Wahrscheinlichkeiten, Unabhängigkeit, Irrfahrten, erzeugende Funktionen, eventuell Markovketten. - Allgemeine Wahrscheinlichkeitsräume: Axiome von Kolmogorov, Zufallsvariablen und ihre Verteilungen, Erwartungswert und andere Kennzahlen, Entropie, charakteristische Funktionen, mehrdimensionale Verteilung inkl. Normalverteilung, Summen von Zufallsvariablen. - Grenzwertsätze: Schwaches und starkes Gesetz der grossen Zahlen, zentraler Grenzwertsatz. - Statistik: Fragestellungen der Statistik (Schätzen, Vertrauensintervalle, Testen), Verknüpfung Statistik und Wahrscheinlichkeit, Neyman-Pearson Lemma, Wilcoxon-, t- und Chiquadrat-Test, Beurteilung von Schätzern, kleinste Quadrate. | ||||
| Literature | "Fundamentals of Probability: a First Course" by Anirban DasGupta Springer 2010 | ||||
| 401-4910-18L | Topics in Mathematical Finance  Number of participants limited to 20. | 4 credits | 2S | J. Teichmann | |
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| 401-5820-00L | Seminar in Computational Finance for CSE | 4 credits | 2S | J. Teichmann | |
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| 401-5910-00L | Talks in Financial and Insurance Mathematics  | 0 credits | 1K | P. Cheridito, P. Embrechts, M. Schweizer, M. Soner, J. Teichmann, M. V. Wüthrich | |
| Abstract | Research colloquium | ||||
| Learning objective | Introduction to current research topics in "Insurance Mathematics and Stochastic Finance". | ||||
| Content | https://www.math.ethz.ch/imsf/courses/talks-in-imsf.html | ||||
| 406-2604-AAL | Probability and Statistics Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 7 credits | 15R | J. Teichmann | |
| Abstract | Introduction 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. | ||||
| Learning objective | The 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. | ||||
| Content | Probability: 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". | ||||
| Literature | Geoffrey 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. | ||||