## Josef Teichmann: Catalogue data in Spring Semester 2021 |

Name | Prof. Dr. Josef Teichmann |

Field | Financial Mathematics |

Address | Professur für Finanzmathematik ETH Zürich, HG G 54.2 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 31 74 |

josef.teichmann@math.ethz.ch | |

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

Department | Mathematics |

Relationship | Full Professor |

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

363-1153-00L | New Technologies in Banking and Finance | 3 credits | 2V | B. J. Bergmann, P. Cheridito, H. Gersbach, P. Mangold, J. Teichmann, R. Wattenhofer | |

Abstract | Technological advances, digitization and the ability to store and process vast amounts of data has changed the landscape of banking and finance in recent years. This course will unpack the technologies underlying these transformations and reflect on the impacts on the financial world, covering also change management perspectives. | ||||

Objective | After taking this course, students will be able to - Understand recent technological developments and how they drive transformation in banking and finance - Understand the challenges of this digital transformation when managing financial and non-financial risks - Reflect on the impacts this transformation has on workflows, agile working, project and change management | ||||

Content | The financial manager of the future is commanding a wide set of skills ranging from a profound understanding of technological advances and a sensible understanding of the impact on workflows and business models. Students with an interest in finance and banking are invited to take the course without explicit theoretical knowledge in financial economics. As the course will cover topics like machine learning, cyber security, distributed computing, and more, an understanding of these technologies is welcomed, however not mandatory. The course will also go beyond technological advances and will also cover management-related contents. The course is divided in sections, each covering different areas and technologies. Students are asked to solve small cases in groups for each section. Invited guest speakers will contribute to the sessions. In addition, separate networking sessions will provide entry opportunities into finance and banking. More information on the speakers and specific session can be found here: https://riskcenter.ethz.ch/education/lectures.html and on the moodle page. | ||||

Prerequisites / Notice | The course is opened to students from all backgrounds. Some experience with quantitative disciplines such as probability and statistics, however, is useful. | ||||

401-2604-00L | Probability and Statistics | 7 credits | 4V + 2U | J. Teichmann | |

Abstract | - Discrete probability spaces - Continuous models - Limit theorems - Introduction to statistics | ||||

Objective | The goal of this course is to provide an introduction to the basic ideas and concepts from probability theory and mathematical statistics. This includes a mathematically rigorous treatment as well as intuition and getting acquainted with the ideas behind the definitions. The course does not use measure theory systematically, but does point out where this is required and what the connections are. | ||||

Content | - Discrete probability spaces: Basic concepts, Laplace models, random walks, conditional probabilities, independence - Continuous models: general probability spaces, random variables and their distributions, expectation, multivariate random variables - Limit theorems: weak and strong law of large numbers, central limit theorem - Introduction to statistics: What is statistics?, point estimators, statistical tests, confidence intervals | ||||

Lecture notes | There will be lecture notes (in German) that are continuously updated during the semester. | ||||

Literature | A. DasGupta, Fundamentals of Probability: A First Course, Springer (2010) J. A. Rice, Mathematical Statistics and Data Analysis, Duxbury Press, second edition (1995) | ||||

401-3932-19L | Machine Learning in Finance | 6 credits | 3V + 1U | J. Teichmann | |

Abstract | The course will deal with the following topics with rigorous proofs and many coding excursions: Universal approximation theorems, Stochastic gradient Descent, Deep networks and wavelet analysis, Deep Hedging, Deep calibration, Different network architectures, Reservoir Computing, Time series analysis by machine learning, Reinforcement learning, generative adversersial networks, Economic games. | ||||

Objective | |||||

Prerequisites / Notice | Bachelor in mathematics, physics, economics or computer science. | ||||

401-4611-21L | Rough Path Theory | 4 credits | 2V | A. Allan, J. Teichmann | |

Abstract | The aim of this course is to provide an introduction to the theory of rough paths, with a particular focus on their integration theory and associated rough differential equations, and how the theory relates to and enhances the field of stochastic calculus. | ||||

Objective | Our first motivation will be to understand the limitations of classical notions of integration to handle paths of very low regularity, and to see how the rough integral succeeds where other notions fail. We will construct rough integrals and establish solutions of differential equations driven by rough paths, as well as the continuity of these objects with respect to the paths involved, and their consistency with stochastic integration and SDEs. Various applications and extensions of the theory will then be discussed. | ||||

Lecture notes | Lecture notes will be provided by the lecturer. | ||||

Literature | P. K. Friz and M. Hairer, A course on rough paths with an introduction to regularity structures, Springer (2014). P. K. Friz and N. B. Victoir. Multidimensional stochastic processes as rough paths, Cambridge University Press (2010). | ||||

Prerequisites / Notice | The aim will be to make the course as self-contained as possible, but some knowledge of stochastic analysis is highly recommended. The course “Brownian Motion and Stochastic Calculus” would be ideal, but not strictly required. | ||||

401-5820-00L | Seminar in Computational Finance for CSE | 4 credits | 2S | J. Teichmann | |

Abstract | |||||

Objective | |||||

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 | ||||

Objective | Introduction to current research topics in "Insurance Mathematics and Stochastic Finance". | ||||

Content | https://www.math.ethz.ch/imsf/courses/talks-in-imsf.html | ||||

406-2604-AAL | Probability and StatisticsEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 7 credits | 15R | J. Teichmann | |

Abstract | - Statistical models - Methods of moments - Maximum likelihood estimation - Hypothesis testing - Confidence intervals - Introductory Bayesian statistics - Linear regression model - Rudiments of high-dimensional statistics | ||||

Objective | The goal of this part of the course is to provide a solid introduction into statistics. It offers of a wide overview of the main tools used in statistical inference. The course will start with an introduction to statistical models and end with some notions of high-dimensional statistics. Some time will be spent on proving certain important results. Tools from probability and measure theory will be assumed to be known and hence will be only and occasionally recalled. | ||||

Lecture notes | Script of Prof. Dr. S. van de Geer | ||||

Literature | These references could be use complementary sources: R. Berger and G. Casella, Statistical Inference J. A. Rice, Mathematical Statistics and Data Analysis L. Wasserman, All of Statistics |