Christoph Schwab: Katalogdaten im Herbstsemester 2023 |
| Name | Herr Prof. Dr. Christoph Schwab |
| Lehrgebiet | Mathematik |
| Adresse | Seminar für Angewandte Mathematik ETH Zürich, HG G 57.1 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telefon | +41 44 632 35 95 |
| Fax | +41 44 632 10 85 |
| christoph.schwab@sam.math.ethz.ch | |
| URL | http://www.sam.math.ethz.ch/~schwab |
| Departement | Mathematik |
| Beziehung | Ordentlicher Professor |
| Nummer | Titel | ECTS | Umfang | Dozierende | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| 401-2653-21L | Numerische Mathematik I  | 7 KP | 3V + 2U | C. Schwab | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Dieser Kurs gibt eine Einführung in mathematische Grundlangen von numerischen Methoden für Studierende der Mathematik im 3. Semester. Abgedeckt werden Methoden der linearen Algebra (lineare Gleichungssysteme, Matrixeigenwertprobleme) sowie der Analysis (Nullstellensuche von Funktionen sowie numerische Interpolation, Integration und Approximation) in Theorie und Implementierung. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | Kenntnis der grundlegenden numerischen Verfahren sowie `numerische Kompetenz': Anwendung der numerischen Verfahren zur Problemloesung, Mathematische Beweistechniken fuer den Nachweis von Stabilitaet, Konsistenz u. Konvergenz der Verfahren sowie deren MATLAB Implementierung. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | Rundungsfehler, lineare Gleichungssysteme, nichtlineare Gleichungen (Skalar und Systeme), Interpolation, Extrapolation, lineare und nichtlineare Ausgleichsrechnung, elementare Optimierungsverfahren, numerische Integration. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | Skript zur Vorlesung sowie Leseliste sind auf der Webseite der Vorlesung verfügbar. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | Skript wird eingeschriebenen Studierenden des ETH BSc Mathematik zur Verfuegung gestellt. _Zusaetzlich_ wird empfohlen: Quarteroni, Sacco und Saleri, Numerische Mathematik 1 + 2, Springer Verlag 2002. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Zulassungsbedingungen: bestandene Pruefungen Lineare Algebra I , Analysis I in ETH BSc MATH u. Linear Algebra II, Analysis II in ETH BSc MATH Woechentliche Hausuebungsserien sind integraler Bestandteil des Kurses; die Hausuebungen involvieren MATLAB Programmieraufgaben, u. werden bewertet. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 401-3650-73L | Numerical Analysis Seminar: ...  Findet dieses Semester nicht statt. | 4 KP | 2S | C. Schwab | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 401-4657-DRL | Numerical Solution of Stochastic Ordinary Differential Equations Alternative course titles: "Numerical Analysis of Stochastic Ordinary Differential Equations" / "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" Only for ZGSM (ETH D-MATH and UZH I-MATH) doctoral students. The latter need to register at myStudies and then send an email to info@zgsm.ch with their name, course number and student ID. Please see https://zgsm.math.uzh.ch/index.php?id=forum0 | 3 KP | 3V + 1U | C. Schwab | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | This course is on the numerical approximations of stochastic ordinary differential equations (SDEs) driven by Brownian motions and Lévy processes. SDEs have several applications, for example in financial engineering. The contents cover stochastic processes, stochastic calculus, well-posedness results for SDEs, strong and weak approximations of SDEs, and simulation via Monte Carlo methods. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | Brownian motion and Lévy processes Stochastic integration and stochastic calculus Stochastic ordinary differential equations (SDEs) Numerical approximations of SDEs Stochastic simulation and Monte Carlo methods Applications to computational finance: Option valuation | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | There will be English, typed lecture notes for registered participants in the course. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992. P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. D. Applebaum: Lévy Processes and Stochastic Calculus. Cambridge University Press, 2009. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Prerequisites: Mandatory: Probability and measure theory, basic numerical analysis and basics of MATLAB/Python programming. a) mandatory courses: Elementary Probability, Probability Theory I. b) recommended courses: Stochastic Processes. Start of lectures: Wednesday September 21, 2022. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 401-4657-00L | Numerical Solution of Stochastic Ordinary Differential Equations Alternative course titles: "Numerical Analysis of Stochastic Ordinary Differential Equations" / "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" | 6 KP | 3V + 1U | C. Schwab | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | This course is on the numerical approximations of stochastic ordinary differential equations (SDEs) driven by Brownian motions and Lévy processes. SDEs have several applications, for example in financial engineering. The contents cover stochastic processes, stochastic calculus, well-posedness results for SDEs, strong and weak approximations of SDEs, and simulation via Monte Carlo methods. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Lernziel | The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Inhalt | Brownian motion and Lévy processes Stochastic integration and stochastic calculus Stochastic ordinary differential equations (SDEs) Numerical approximations of SDEs Stochastic simulation and Monte Carlo methods Applications to computational finance: Option valuation | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skript | There will be English, typed lecture notes for registered participants in the course. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Literatur | P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992. P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. D. Applebaum: Lévy Processes and Stochastic Calculus. Cambridge University Press, 2009. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Voraussetzungen / Besonderes | Prerequisites: Mandatory: Probability and measure theory, basic numerical analysis and basics of MATLAB/Python programming. a) mandatory courses: Elementary Probability, Probability Theory I. b) recommended courses: Stochastic Processes. Start of lectures: Wednesday September 21, 2022. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kompetenzen |
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| 401-5650-00L | Zurich Colloquium in Applied and Computational Mathematics | 0 KP | 1K | R. Abgrall, R. Alaifari, H. Ammari, R. Hiptmair, S. Mishra, S. Sauter, C. Schwab | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Kurzbeschreibung | Research colloquium | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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