## Martin Larsson: Catalogue data in Spring Semester 2019 |

Name | Dr. Martin Larsson |

Field | Mathematical Finance |

URL | http://www.math.ethz.ch/~larssonm |

Department | Mathematics |

Relationship | Assistant Professor |

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

364-1058-00L | Risk Center Seminar Series Number of participants limited to 50. | 0 credits | 2S | A. Bommier, D. Basin, D. N. Bresch, L.‑E. Cederman, P. Cheridito, H. Gersbach, H. R. Heinimann, M. Larsson, G. Sansavini, F. Schweitzer, D. Sornette, B. Stojadinovic, B. Sudret, U. A. Weidmann, S. Wiemer, M. Zeilinger, R. Zenklusen | |

Abstract | This course is a mixture between a seminar primarily for PhD and postdoc students and a colloquium involving invited speakers. It consists of presentations and subsequent discussions in the area of modeling and governing complex socio-economic systems, and managing risks and crises. Students and other guests are welcome. | ||||

Objective | Participants should learn to get an overview of the state of the art in the field, to present it in a well understandable way to an interdisciplinary scientific audience, to develop novel mathematical models and approaches for open problems, to analyze them with computers or other means, and to defend their results in response to critical questions. In essence, participants should improve their scientific skills and learn to work scientifically on an internationally competitive level. | ||||

Content | This course is a mixture between a seminar primarily for PhD and postdoc students and a colloquium involving invited speakers. It consists of presentations and subsequent discussions in the area of modeling complex socio-economic systems and crises. For details of the program see the webpage of the seminar. Students and other guests are welcome. | ||||

Lecture notes | There is no script, but the sessions will be recorded and be made available. Transparencies of the presentations may be put on the course webpage. | ||||

Literature | Literature will be provided by the speakers in their respective presentations. | ||||

Prerequisites / Notice | Participants should have relatively good scientific, in particular mathematical skills and some experience of how scientific work is performed. | ||||

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. Larsson | |

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 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 | ||||

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 https://www.math.ethz.ch/imsf/education/education-in-stochastic-finance/overview-of-courses.html. |