# 401-3888-00L Introduction to Mathematical Finance

Semester | Spring Semester 2019 |

Lecturers | M. Larsson |

Periodicity | yearly recurring course |

Language of instruction | English |

Comment | 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. |

### Catalogue data

Abstract | 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. We prove the fundamental theorem of asset pricing and the hedging duality theorems, and also study convex duality in utility maximization. |

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 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 an overview of courses offered in the area of mathematical finance, see Link. |

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 |

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 other words, it is also not possible to earn credit points with one for the Bachelor and with the other 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 Link. |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 10 credits |

Examiners | M. Schweizer |

Type | session examination |

Language of examination | English |

Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |

Mode of examination | oral 30 minutes |

This information can be updated until the beginning of the semester; information on the examination timetable is binding. |

### Learning materials

Main link | Introduction to Mathematical Finance |

Only public learning materials are listed. |

### Courses

Number | Title | Hours | Lecturers | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

401-3888-00 V | Introduction to Mathematical Finance | 4 hrs |
| M. Larsson | ||||||||||||

401-3888-00 U | Introduction to Mathematical Finance Wed 14-15 or Wed 15-16 | 1 hrs |
| M. Larsson |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |

### Offered in

Programme | Section | Type | |
---|---|---|---|

Data Science Master | Interdisciplinary Electives | W | |

Mathematics Bachelor | Selection: Financial and Insurance Mathematics | W | |

Mathematics Master | Selection: Financial and Insurance Mathematics | W |