## Beatrice Acciaio: Catalogue data in Autumn Semester 2023 |

Name | Prof. Dr. Beatrice Acciaio |

Field | Mathematics |

Address | Professur für Mathematik ETH Zürich, HG G 54.3 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 29 55 |

beatrice.acciaio@math.ethz.ch | |

URL | https://people.math.ethz.ch/~beacciaio/ |

Department | Mathematics |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |||||||||||||||||||||||||||||
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401-3913-01L | Mathematical Foundations for Finance | 4 credits | 3V + 2U | B. Acciaio | |||||||||||||||||||||||||||||

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

Learning 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 | See information on course homepage | ||||||||||||||||||||||||||||||||

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. | ||||||||||||||||||||||||||||||||

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

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