## Martin Schweizer: Catalogue data in Spring Semester 2022 |

Name | Prof. Dr. Martin Schweizer |

Field | Mathematik |

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 | |
---|---|---|---|---|---|

401-3642-DRL | Brownian Motion and Stochastic Calculus 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 (Link) with the course number. The email should have the subject „Graduate course registration (ETH)“. | 2 credits | 4V + 1U | M. Schweizer | |

Abstract | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | ||||

Objective | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | ||||

Lecture notes | Lecture notes will be distributed in class. | ||||

Literature | - J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). - I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). - 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). - D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer (2006). | ||||

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). | ||||

401-3642-00L | Brownian Motion and Stochastic Calculus | 10 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. | ||||

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). | ||||

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 | ||||

Objective | Introduction to current research topics in "Insurance Mathematics and Stochastic Finance". | ||||

Content | https://www.math.ethz.ch/imsf/courses/talks-in-imsf.html |