Martin Schweizer: Catalogue data in Spring Semester 2025 |
| Name | Prof. Dr. Martin Schweizer |
| Field | Mathematics |
| Address | Professur für Mathematik ETH Zürich, HG G 51.2 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 632 33 51 |
| Fax | +41 44 632 14 74 |
| martin.schweizer@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~mschweiz |
| Department | Mathematics |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |||||||||||||||||
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| 401-3642-00L | Brownian Motion and Stochastic Calculus  | 9 credits | 4V + 1U | M. Schweizer | |||||||||||||||||
| Abstract | This course gives an introduction to Brownian motion and stochastic calculus. It includes the construction and properties of Brownian motion, basics of Markov processes in continuous time and of Levy processes, and stochastic calculus for continuous semimartingales. | ||||||||||||||||||||
| Learning objective | This course gives an introduction to Brownian motion and stochastic calculus. The following topics are planned: - Definition and construction of Brownian motion - Some important properties of Brownian motion - Basics of Markov processes in continuous time - Stochastic calculus, including stochastic integration for continuous semimartingales, Ito's formula, Girsanov's theorem, stochastic differential equations and connections with partial differential equations - Basics of Levy processes | ||||||||||||||||||||
| Lecture notes | Lecture notes will be made available in class. | ||||||||||||||||||||
| Literature | - R.F. Bass, Stochastic Processes, Cambidge University Press (2001). - I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). - J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). - D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005). - L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000). | ||||||||||||||||||||
| Prerequisites / Notice | Familiarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in - J. Jacod, P. Protter, Probability Essentials, Springer (2004). - R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010). | ||||||||||||||||||||
| Competencies |
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| 401-5910-00L | Talks in Financial and Insurance Mathematics | 0 credits | 1K | B. Acciaio, P. Cheridito, D. Possamaï, M. Schweizer, 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 | ||||||||||||||||||||