# Search result: Catalogue data in Autumn Semester 2018

Mathematics Master | ||||||

Electives For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields. | ||||||

Electives: Applied Mathematics and Further Application-Oriented Fields ¬ | ||||||

Selection: Financial and Insurance Mathematics In the Master's programmes in Mathematics resp. Applied Mathematics 401-3913-01L Mathematical Foundations for Finance is eligible as an elective course, but only if 401-3888-00L Introduction to Mathematical Finance isn't recognised for credits (neither in the Bachelor's nor in the Master's programme). For the category assignment take contact with the Study Administration Office (Link) after having received the credits. | ||||||

Number | Title | Type | ECTS | Hours | Lecturers | |
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401-3925-00L | Non-Life Insurance: Mathematics and Statistics | W | 8 credits | 4V + 1U | M. V. Wüthrich | |

Abstract | The lecture aims at providing a basis in non-life insurance mathematics which forms a core subject of actuarial sciences. It discusses collective risk modeling, individual claim size modeling, approximations for compound distributions, ruin theory, premium calculation principles, tariffication with generalized linear models, credibility theory, claims reserving and solvency. | |||||

Objective | The student is familiar with the basics in non-life insurance mathematics and statistics. This includes the basic mathematical models for insurance liability modeling, pricing concepts, stochastic claims reserving models and ruin and solvency considerations. | |||||

Content | The following topics are treated: Collective Risk Modeling Individual Claim Size Modeling Approximations for Compound Distributions Ruin Theory in Discrete Time Premium Calculation Principles Tariffication and Generalized Linear Models Bayesian Models and Credibility Theory Claims Reserving Solvency Considerations | |||||

Lecture notes | M. V. Wüthrich, Non-Life Insurance: Mathematics & Statistics Link | |||||

Prerequisites / Notice | The exams ONLY take place during the official ETH examination period. This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under Link. Prerequisites: knowledge of probability theory, statistics and applied stochastic processes. | |||||

401-3922-00L | Life Insurance Mathematics | W | 4 credits | 2V | M. Koller | |

Abstract | The classical life insurance model is presented together with the important insurance types (insurance on one and two lives, term and endowment insurance and disability). Besides that the most important terms such as mathematical reserves are introduced and calculated. The profit and loss account and the balance sheet of a life insurance company is explained and illustrated. | |||||

Objective | ||||||

401-3928-00L | Reinsurance Analytics | W | 4 credits | 2V | P. Antal, P. Arbenz | |

Abstract | This course provides an actuarial introduction to reinsurance. The objective is to understand the fundamentals of risk transfer through reinsurance, and the mathematical models for extreme events such as natural or man-made catastrophes. The lecture covers reinsurance contracts, Experience and Exposure pricing, natural catastrophe modelling, solvency regulation, and alternative risk transfer | |||||

Objective | This course provides an introduction to reinsurance from an actuarial point of view. The objective is to understand the fundamentals of risk transfer through reinsurance, and the mathematical approaches associated with low frequency high severity events such as natural or man-made catastrophes. Topics covered include: - Reinsurance Contracts and Markets: Different forms of reinsurance, their mathematical representation, history of reinsurance, and lines of business. - Experience Pricing: Modelling of low frequency high severity losses based on historical data, and analytical tools to describe and understand these models - Exposure Pricing: Loss modelling based on exposure or risk profile information, for both property and casualty risks - Natural Catastrophe Modelling: History, relevance, structure, and analytical tools used to model natural catastrophes in an insurance context - Solvency Regulation: Regulatory capital requirements in relation to risks, effects of reinsurance thereon, and differences between the Swiss Solvency Test and Solvency 2 - Alternative Risk Transfer: Alternatives to traditional reinsurance such as insurance linked securities and catastrophe bonds | |||||

Content | This course provides an introduction to reinsurance from an actuarial point of view. The objective is to understand the fundamentals of risk transfer through reinsurance, and the mathematical approaches associated with low frequency high severity events such as natural or man-made catastrophes. Topics covered include: - Reinsurance Contracts and Markets: Different forms of reinsurance, their mathematical representation, history of reinsurance, and lines of business. - Experience Pricing: Modelling of low frequency high severity losses based on historical data, and analytical tools to describe and understand these models - Exposure Pricing: Loss modelling based on exposure or risk profile information, for both property and casualty risks - Natural Catastrophe Modelling: History, relevance, structure, and analytical tools used to model natural catastrophes in an insurance context - Solvency Regulation: Regulatory capital requirements in relation to risks, effects of reinsurance thereon, and differences between the Swiss Solvency Test and Solvency 2 - Alternative Risk Transfer: Alternatives to traditional reinsurance such as insurance linked securities and catastrophe bonds | |||||

Lecture notes | Slides, lecture notes, and references to literature will be made available. | |||||

Prerequisites / Notice | Basic knowledge in statistics, probability theory, and actuarial techniques | |||||

401-3927-00L | Mathematical Modelling in Life Insurance | W | 4 credits | 2V | T. J. Peter | |

Abstract | In Life insurance, it is essential to have adequate mortality tables, be it for reserving or pricing purposes. We learn to create mortality tables from scratch. Additionally, we study various guarantees embedded in life insurace products and learn to price them with the help of stochastic models. | |||||

Objective | The course's objective is to provide the students with the understanding and the tools to create mortality tables on their own. Additionally, students should learn to price embedded options in Life insurance. Aside of the mere application of specific models, they should develop an intuition for the various drivers of the value of these options. | |||||

Content | Following main topics are covered: 1. Overview on guarantees & options in life insurance with a real-world example demonstrating their risks 2. Mortality tables - Determining raw mortality rates - Smoothing of raw mortality rates - Trends in mortality rates - Lee-Carter model - Integration of safety margins 3. Primer on Financial Mathematics - Ito integral - Black-Scholes and Hull-White model 4. Valuation of Unit linked contracts with embedded options 5. Valuation of Participating contracts | |||||

Lecture notes | Lectures notes and slides will be provided | |||||

Prerequisites / Notice | The exams ONLY take place during the official ETH examination period. The course counts towards the diploma of "Aktuar SAV". Good knowledge in probability theory and stochastic processes is assumed. Some knowledge in financial mathematics is useful. | |||||

401-4912-11L | Trends in Stochastic Portfolio Theory | W | 4 credits | 2V | M. Larsson | |

Abstract | This course presents an introduction to Stochastic Portfolio Theory, which provides a mathematical framework for studying and exploiting empirically observed regularities of large equity markets. A central goal of the theory is to describe certain forms of arbitrage that arise over sufficiently long time horizons. | |||||

Objective | ||||||

Content | This course presents an introduction to Stochastic Portfolio Theory, which provides a mathematical framework for studying and exploiting empirically observed regularities of large equity markets. A central goal of the theory is to describe certain forms of arbitrage that arise over sufficiently long time horizons. Since it was first introduced by Robert Fernholz almost 20 years ago, the theory has experienced rapid developments. This course will cover the foundations of Stochastic Portfolio Theory, including topics like relative arbitrage, functional portfolio generation, and capital distribution curves, as well as more recent developments. | |||||

Prerequisites / Notice | Prerequisites: Familiarity with Ito calculus at the level of Brownian Motion and Stochastic Calculus. Some background in mathematical finance is helpful. A course with similar content was offered in HS 2015 under the title "New Trends in Stochastic Portfolio Theory". | |||||

401-3905-68L | Convex Optimization in Machine Learning and Computational Finance | W | 4 credits | 2V | P. Cheridito, M. Baes | |

Abstract | ||||||

Objective | ||||||

Content | Part 1: Convex Analysis Lecture 1: General introduction, convex sets and functions Lecture 2: Semidefinite cone, Separation theorems (Application to the Fundamental Theorem of Asset Pricing) Lecture 3: Analytic properties of convex functions, duality (Application to Support Vector Machines) Lecture 4: Lagrangian duality, conjugate functions, support functions Lecture 5: Subgradients and subgradient calculus (Application to Automatic Differentiation and Lexicographic Differentiation) Lecture 6: Karush-Kuhn-Tucker Conditions (Application to Markowitz portfolio optimization) Part 2: Applications Lecture 7: Approximation, Lasso optimization, Covariance matrix estimation (Application: a politically optimal splitting of Switzerland) Lecture 8: Clustering and MaxCut problems, Optimal coalitions and Shapley Value Part 3: Algorithms Lecture 9: Intractability of Optimization, Gradient Method for convex optimization, Stochastic Gradient Method (Application to Neural Networks) Lecture 10: Fundamental flaws of Gradient Methods, Mirror Descent Method (Application to Multiplicative Weight Method and Adaboost) Lecture 11: Accelerated Gradient Method, Smoothing Technique (Application to large-scale Lasso optimization) Lecture 12: Newton Method and its fundamental drawbacks, Self-Concordant Functions Lecture 13: Interior-Point Methods |

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