## Martin Schweizer: Catalogue data in Autumn Semester 2017 |

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

401-0603-00L | Stochastics (Probability and Statistics) | 4 credits | 2V + 1U | M. Schweizer | |

Abstract | This class covers the following concepts: random variables, probability, discrete and continuous distributions, joint and conditional probabilities and distributions, the law of large numbers, the central limit theorem, descriptive statistics, statistical inference, inference for normally distributed data, point estimation, and two-sample tests. | ||||

Objective | Knowledge of the basic principles of probability and statistics. | ||||

Content | Introduction to probability theory, some basic principles from mathematical statistics and basic methods for applied statistics. | ||||

Lecture notes | Lecture notes | ||||

Literature | Lecture notes | ||||

401-3913-01L | Mathematical Foundations for Finance | 4 credits | 3V + 2U | M. Schweizer, E. W. Farkas | |

Abstract | First introduction to main modelling ideas and mathematical tools from mathematical finance | ||||

Objective | This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It mainly aims at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest.. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs. | ||||

Content | Topics to be covered include - financial market models in finite discrete time - absence of arbitrage and martingale measures - valuation and hedging in complete markets - basics about Brownian motion - stochastic integration - stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem - Black-Scholes formula | ||||

Lecture notes | Lecture notes will be sold at the beginning of the course. | ||||

Literature | Lecture notes will be sold at the beginning of the course. Additional (background) references are given there. | ||||

Prerequisites / Notice | Prerequisites: Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely. Especially participants without a direct mathematics background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. (A possible alternative to the above English textbook are the (German) lecture notes for the standard course "Wahrscheinlichkeitstheorie".) For those who are not sure about their background, we suggest to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared. | ||||

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 | ||||

Objective | |||||

Content | Regular research talks on various topics in mathematical finance and actuarial mathematics | ||||

406-2284-AAL | Measure and IntegrationEnrolment 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. | 6 credits | 13R | M. Schweizer | |

Abstract | Introduction to the abstract measure theory and integration, including the following topics: Lebesgue measure and Lebesgue integral, Lp-spaces, convergence theorems, differentiation of measures, product measures (Fubini's theorem), abstract measures, Radon-Nikodym theorem, probabilistic language. | ||||

Objective | Basic acquaintance with the theory of measure and integration, in particular, Lebesgue's measure and integral. | ||||

Literature | 1. Lecture notes by Professor Michael Struwe (http://www.math.ethz.ch/~struwe/Skripten/AnalysisIII-SS2007-18-4-08.pdf) 2. L. Evans and R.F. Gariepy "Measure theory and fine properties of functions" 3. Walter Rudin "Real and complex analysis" 4. R. Bartle The elements of Integration and Lebesgue Measure 5. P. Cannarsa & T. D'Aprile: Lecture notes on Measure Theory and Functional Analysis. http://www.mat.uniroma2.it/~cannarsa/cam_0607.pdf |