## Martin Schweizer: Catalogue data in Spring Semester 2023 |

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 | |||||||||||||||||||||||||||||
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401-3888-00L | Introduction to Mathematical Finance A related course is 401-3913-01L Mathematical Foundations for Finance (3V+2U, 4 ECTS credits). Although both courses can be taken independently of each other, only one will be recognised for credits in the Bachelor and Master degree. In other words, it is not allowed to earn credit points with one for the Bachelor and with the other for the Master degree. | 10 credits | 4V + 1U | M. Schweizer | |||||||||||||||||||||||||||||

Abstract | Introductory course on mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. Topics: arbitrage, completeness, risk-neutral pricing, utility maximisation, and maybe others. Fundamental theorem of asset pricing, hedging duality theorems in discrete time, convex duality in utility maximisation. | ||||||||||||||||||||||||||||||||

Objective | This is an introductory course on the mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. We discuss arbitrage, completeness, risk-neutral pricing and utility maximisation, and maybe other topics. We prove the fundamental theorem of asset pricing and the hedging duality theorems in discrete time, and we also study convex duality in utility maximization. | ||||||||||||||||||||||||||||||||

Content | This course focuses on discrete-time financial markets. It presumes a knowledge of measure-theoretic probability theory (as taught e.g. in the course "Probability Theory"). The course is offered every year in the Spring semester. This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MF II), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MF I, is taken prior to MF II. For a (not fully up-to-date) 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. | ||||||||||||||||||||||||||||||||

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

Literature | Literature: Michael U. Dothan, "Prices in Financial Markets", Oxford University Press Hans Föllmer and Alexander Schied, "Stochastic Finance: An Introduction in Discrete Time", de Gruyter Marek Capinski and Ekkehard Kopp, "Discrete Models of Financial Markets", Cambridge University Press Robert J. Elliott and P. Ekkehard Kopp, "Mathematics of Financial Markets", Springer Dmitry Kramkov and Walter Schachermayer, "The asymptotic elasticity of utility functions and optimal investment in incomplete markets", Annals of Applied Probability 9 (1999), 904-950 | ||||||||||||||||||||||||||||||||

Prerequisites / Notice | A related course is "Mathematical Foundations for Finance" (MFF), 401-3913-01. Although both courses can be taken independently of each other, only one will be given credit points for the Bachelor and the Master degree. In particular, it is not possible to earn credit points with one course for the Bachelor and with the other course for the Master degree. This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MF II), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MF I, is taken prior to 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. | ||||||||||||||||||||||||||||||||

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 | ||||||||||||||||||||||||||||||||

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

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