# 401-4889-00L Mathematical Finance

Semester | Autumn Semester 2019 |

Lecturers | J. Teichmann |

Periodicity | yearly recurring course |

Language of instruction | English |

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 Link. |