Christoph Schwab: Katalogdaten im Frühjahrssemester 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 | |
|---|---|---|---|---|---|
| 401-3650-23L | Numerical Analysis Seminar: Deep Neural Network Methods for PDEs  Number of Participants: limited to seven. Participation by consent of instructor. | 4 KP | 2S | C. Schwab | |
| Kurzbeschreibung | The seminar will review recent _mathematical results_ on approximation power of deep neural networks (DNNs). The focus will be on mathematical proof techniques to obtain approximation rate estimates (in terms of neural network size and connectivity) on various classes of input data including, in particular, selected types of PDE solutions. | ||||
| Lernziel | |||||
| Inhalt | Deep Neural Networks (DNNs) have recently attracted substantial interest and attention due to outperforming the best established techniques in a number of tasks (Chess, Go, Shogi, autonomous driving, language translation, image classification, etc.). In big data analysis, DNNs achieved remarkable performance in computer vision, speech recognition and natural language processing. In many cases, these successes have been achieved by heuristic implementations combined with massive compute power and training data. For a (bird's eye) view, see https://doi.org/10.1017/9781108860604 and, more mathematical and closer to the seminar theme, https://doi.org/10.1109/TIT.2021.3062161 The seminar will review recent _mathematical results_ on approximation power of deep neural networks (DNNs). The focus will be on mathematical proof techniques to obtain approximation rate estimates (in terms of neural network size and connectivity) on various classes of input data including, in particular, selected types of PDE solutions. Mathematical results support that DNNs can equalize or outperform the best mathematical results known to date. Particular cases comprise: high-dimensional parametric maps, analytic and holomorphic maps, maps containing multi-scale features which arise as solution classes from PDEs, classes of maps which are invariant under group actions. Format of the Seminar: The seminar format will be oral student presentations, combined with written report. Student presentations will be based on a recent research paper selected in two meetings at the start of the semester. Grading of the Seminar: Passing grade will require a) 1hr oral presentation _via Zoom_ with Q/A from the seminar group, in early May 2022 and b) typed seminar report (``Ausarbeitung'') of several key aspects of the paper under review. Each seminar topic will allow expansion to a semester or a master thesis in the MSc MATH or MSc Applied MATH. Disclaimer: The seminar will _not_ address recent developments in DNN software, eg. TENSORFLOW, and algorithmic training heuristics, or programming techniques for DNN training in various specific applications. | ||||
| 401-4658-DRL | Numerical Methods for Finance Only for ETH D-MATH doctoral students and for doctoral students from the Institute of Mathematics at UZH. The latter need to send an email to Jessica Bolsinger (info@zgsm.ch) with the course number. The email should have the subject „Graduate course registration (ETH)“. | 3 KP | 3V + 1U | C. Schwab, A. Stein | |
| Kurzbeschreibung | TO BE ADJUSTED Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB and Python programming and knowledge of numerical mathematics at ETH BSc level. | ||||
| Lernziel | Introduce the main methods for efficient numerical valuation of derivative contracts in a Black Scholes as well as in incomplete markets due Levy processes or due to stochastic volatility models. Develop implementation of pricing methods in MATLAB and Python. Finite-Difference/ Finite Element based methods for the solution of the pricing integrodifferential equation. | ||||
| Inhalt | TO BE ADJUSTED 1. Review of option pricing. Wiener and Levy price process models. Deterministic, local and stochastic volatility models. 2. Finite Difference Methods for option pricing. Relation to bi- and multinomial trees. European contracts. 3. Finite Difference methods for Asian, American and Barrier type contracts. 4. Finite element methods for European and American style contracts. 5. Pricing under local and stochastic volatility in Black-Scholes Markets. 6. Finite Element Methods for option pricing under Levy processes. Treatment of integrodifferential operators. 7. Stochastic volatility models for Levy processes. 8. Techniques for multidimensional problems. Baskets in a Black-Scholes setting and stochastic volatility models in Black Scholes and Levy markets. 9. Introduction to sparse grid option pricing techniques. | ||||
| Skript | There will be english lecture notes as well as MATLAB or Python software for registered participants in the course. | ||||
| Literatur | Main reference (course text): N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013. Supplementary texts: R. Cont and P. Tankov : Financial Modelling with Jump Processes, Chapman and Hall Publ. 2004. Y. Achdou and O. Pironneau : Computational Methods for Option Pricing, SIAM Frontiers in Applied Mathematics, SIAM Publishers, Philadelphia 2005. D. Lamberton and B. Lapeyre : Introduction to stochastic calculus Applied to Finance (second edition), Chapman & Hall/CRC Financial Mathematics Series, Taylor & Francis Publ. Boca Raton, London, New York 2008. J.-P. Fouque, G. Papanicolaou and K.-R. Sircar : Derivatives in financial markets with stochastic volatility, Cambridge Univeristy Press, Cambridge, 2000. | ||||
| Voraussetzungen / Besonderes | Knowledge of Numerical Analysis/ Scientific Computing Techniques corresponding roughly to BSc MATH or BSc RW/CSE at ETH is expected. Basic programming skills in MATLAB or Python are required for the exercises, and are _not_ taught in this course. | ||||
| 401-4658-00L | Numerical Methods for Finance  | 6 KP | 3V + 1U | C. Schwab, A. Stein | |
| Kurzbeschreibung | Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB and Python programming and knowledge of numerical mathematics at ETH BSc level. | ||||
| Lernziel | Introduce the main methods for efficient numerical valuation of derivative contracts in a Black Scholes as well as in incomplete markets due Levy processes or due to stochastic volatility models. Develop implementation of pricing methods in MATLAB and Python. Finite-Difference/ Finite Element based methods for the solution of the pricing integrodifferential equation. | ||||
| Inhalt | 1. Review of option pricing. Wiener and Levy price process models. Deterministic, local and stochastic volatility models. 2. Finite Difference Methods for option pricing. Relation to bi- and multinomial trees. European contracts. 3. Finite Difference methods for Asian, American and Barrier type contracts. 4. Finite element methods for European and American style contracts. 5. Pricing under local and stochastic volatility in Black-Scholes Markets. 6. Finite Element Methods for option pricing under Levy processes. Treatment of integrodifferential operators. 7. Stochastic volatility models for Levy processes. 8. Techniques for multidimensional problems. Baskets in a Black-Scholes setting and stochastic volatility models in Black Scholes and Levy markets. 9. Introduction to sparse grid option pricing techniques. | ||||
| Skript | There will be english lecture notes as well as MATLAB or Python software for registered participants in the course. | ||||
| Literatur | Main reference (course text): N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013. Supplementary texts: R. Cont and P. Tankov : Financial Modelling with Jump Processes, Chapman and Hall Publ. 2004. Y. Achdou and O. Pironneau : Computational Methods for Option Pricing, SIAM Frontiers in Applied Mathematics, SIAM Publishers, Philadelphia 2005. D. Lamberton and B. Lapeyre : Introduction to stochastic calculus Applied to Finance (second edition), Chapman & Hall/CRC Financial Mathematics Series, Taylor & Francis Publ. Boca Raton, London, New York 2008. J.-P. Fouque, G. Papanicolaou and K.-R. Sircar : Derivatives in financial markets with stochastic volatility, Cambridge Univeristy Press, Cambridge, 2000. | ||||
| Voraussetzungen / Besonderes | Knowledge of Numerical Analysis/ Scientific Computing Techniques corresponding roughly to BSc MATH or BSc RW/CSE at ETH is expected. Basic programming skills in MATLAB or Python are required for the exercises, and are _not_ taught in this course. | ||||
| 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 | Forschungskolloquium | ||||
| Lernziel | |||||