## Martin Schweizer: Catalogue data in Autumn Semester 2018 |

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

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

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. | ||||

401-4889-00L | Mathematical Finance | 11 credits | 4V + 2U | M. Schweizer | |

Abstract | Advanced course on mathematical finance: - semimartingales and general stochastic integration - absence of arbitrage and martingale measures - fundamental theorem of asset pricing - option pricing and hedging - hedging duality - optimal investment problems - additional topics | ||||

Objective | Advanced course on mathematical finance, presupposing good knowledge in probability theory and stochastic calculus (for continuous processes) | ||||

Content | This is an advanced course on mathematical finance for students with a good background in probability. We want to give an overview of main concepts, questions and approaches, and we do this mostly in continuous-time models. Topics include - semimartingales and general stochastic integration - absence of arbitrage and martingale measures - fundamental theorem of asset pricing - option pricing and hedging - hedging duality - optimal investment problems - and probably others | ||||

Lecture notes | The course is based on different parts from different books as well as on original research literature. Lecture notes will not be available. | ||||

Literature | (will be updated later) | ||||

Prerequisites / Notice | Prerequisites are the standard courses - Probability Theory (for which lecture notes are available) - Brownian Motion and Stochastic Calculus (for which lecture notes are available) Those students who already attended "Introduction to Mathematical Finance" will have an advantage in terms of ideas and concepts. This course is the second of a sequence of two courses on mathematical finance. The first course "Introduction to Mathematical Finance" (MF I), 401-3888-00, focuses on models in finite discrete time. It is advisable that the course MF I is taken prior to the present course, MF II. For an overview of courses offered in the area of mathematical finance, see https://www.math.ethz.ch/imsf/education/education-in-stochastic-finance/overview-of-courses.html. | ||||

401-5910-00L | Talks in Financial and Insurance Mathematics | 0 credits | 1K | P. Cheridito, 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 |