# 401-3913-01L Mathematical Foundations for Finance

Semester | Autumn Semester 2020 |

Lecturers | M. Schweizer |

Periodicity | yearly recurring course |

Language of instruction | English |

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 aims mainly 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 made available at the beginning of the course. |

Literature | Lecture notes will be made available 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. |