# Search result: Catalogue data in Autumn Semester 2020

Mathematics (General Courses) | ||||||

Actuary SAA Education at ETH Zurich Further pieces of information are available at Prof. M. Wüthrich's secretariat, HG F 42. | ||||||

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 science. It discusses collective risk modeling, individual claim size modeling, approximations for compound distributions, ruin theory, premium calculation principles, tariffication with generalized linear models and neural networks, 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 Generalized Linear Models and Neural Networks 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 | ||||||

401-3929-00L | Financial Risk Management in Social and Pension Insurance | W | 4 credits | 2V | P. Blum | |

Abstract | Investment returns are an important source of funding for social and pension insurance, and financial risk is an important threat to stability. We study short-term and long-term financial risk and its interplay with other risk factors, and we develop methods for the measurement and management of financial risk and return in an asset/liability context with the goal of assuring sustainable funding. | |||||

Objective | Understand the basic asset-liability framework: essential principles and properties of social and pension insurance; cash flow matching, duration matching, valuation portfolio and loose coupling; the notion of financial risk; long-term vs. short-term risk; coherent measures of risk. Understand the conditions for sustainable funding: derivation of required returns; interplay between return levels, contribution levels and other parameters; influence of guaranteed benefits. Understand the notion of risk-taking capability: capital process as a random walk; measures of long-term risk and relation to capital; short-term solvency vs. long-term stability; effect of embedded options and guarantees; interplay between required return and risk-taking capability. Be able to study empirical properties of financial assets: the Normal hypothesis and the deviations from it; statistical tools for investigating relevant risk and return properties of financial assets; time aggregation properties; be able to conduct analysis of real data for the most important asset classes. Understand and be able to carry out portfolio construction: the concept of diversification; limitations to diversification; correlation breakdown; incorporation of constraints; sensitivities and shortcomings of optimized portfolios. Understand and interpret the asset-liability interplay: the optimized portfolio in the asset-liability framework; short-term risk vs. long-term risk; the influence of constraints; feasible and non-feasible solutions; practical considerations. Understand and be able to address essential problems in asset / liability management, e.g. optimal risk / return positioning, optimal discount rate, target value for funding ratio or turnaround issues. Have an overall view: see the big picture of what asset returns can and cannot contribute to social security; be aware of the most relevant outcomes; know the role of the actuary in the financial risk management process. | |||||

Content | For pension insurance and other forms of social insurance, investment returns are an important source of funding. In order to earn these returns, substantial financial risks must be taken, and these risks represent an important threat to financial stability, in the long term and in the short term. Risk and return of financial assets cannot be separated from one another and, hence, asset management and risk management cannot be separated either. Managing financial risk in social and pension insurance is, therefore, the task of reconciling the contradictory dimensions of 1. Required return for a sustainable funding of the institution, 2. Risk-taking capability of the institution, 3. Returns available from financial assets in the market, 4. Risks incurred by investing in these assets. This task must be accomplished under a number of constraints. Financial risk management in social insurance also means reconciling the long time horizon of the promised insurance benefits with the short time horizon of financial markets and financial risk. It is not the goal of this lecture to provide the students with any cookbook recipes that can readily be applied without further reflection. The goal is rather to enable the students to develop their own understanding of the problems and possible solutions associated with the management of financial risks in social and pension insurance. To this end, a rigorous intellectual framework will be developed and a powerful set of mathematical tools from the fields of actuarial mathematics and quantitative risk management will be applied. When analyzing the properties of financial assets, an empirical viewpoint will be taken using statistical tools and considering real-world data. | |||||

Lecture notes | Extensive handouts will be provided. Moreover, practical examples and data sets in Excel and R will be made available. | |||||

Prerequisites / Notice | Solid base knowledge of probability and statistics is indispensable. Specialized concepts from financial and insurance mathematics as well as quantitative risk management will be introduced in the lecture as needed, but some prior knowledge in some of these areas would be an advantage. This course counts towards the diploma of "Aktuar SAV". The exams ONLY take place during the official ETH examination period. | |||||

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

Abstract | This course provides an introduction to reinsurance from an actuarial perspective. The objective is to understand the fundamentals of risk transfer through reinsurance and 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 insurance linked securities | |||||

Objective | This course provides an introduction to reinsurance from an actuarial perspective. 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 - Insurance linked securities: Alternative risk transfer techniques such as catastrophe bonds | |||||

Content | This course provides an introduction to reinsurance from an actuarial perspective. 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 - Insurance linked securities: Alternative risk transfer techniques such as catastrophe bonds | |||||

Lecture notes | Slides and lecture notes will be made available. An excerpt of last year's lecture notes is available here: Link | |||||

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. The course provides the tools necessary to create mortality tables from scratch. Additionally, we study various guarantees embedded in life insurance 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. Guarantees and options embedded in life insurance products. - Stochastic valuation of participating contracts - Stochastic valuation of Unit Linked contracts 2. Mortality Tables: - Determining raw mortality rates - Smoothing techniques: Whittaker-Henderson, smoothing splines,... - Trends in mortality rates - Stochastic mortality model due to Lee and Carter - Neural Network extension of the Lee-Carter model - Integration of safety margins | |||||

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. | |||||

401-3913-01L | Mathematical Foundations for Finance | W | 4 credits | 3V + 2U | M. Schweizer | |

Abstract | First introduction to main modelling ideas and mathematical tools from mathematical finance | |||||

Objective | This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It aims mainly at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs. | |||||

Content | Topics to be covered include - financial market models in finite discrete time - absence of arbitrage and martingale measures - valuation and hedging in complete markets - basics about Brownian motion - stochastic integration - stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem - Black-Scholes formula | |||||

Lecture notes | Lecture notes will be made available at the beginning of the course. | |||||

Literature | Lecture notes will be made available at the beginning of the course. Additional (background) references are given there. | |||||

Prerequisites / Notice | Prerequisites: Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely. Especially participants without a direct mathematics background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. (A possible alternative to the above English textbook are the (German) lecture notes for the standard course "Wahrscheinlichkeitstheorie".) For those who are not sure about their background, we suggest to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared. | |||||

363-0565-00L | Principles of Macroeconomics | W | 3 credits | 2V | J.‑E. Sturm | |

Abstract | This course examines the behaviour of macroeconomic variables, such as gross domestic product, unemployment and inflation rates. It tries to answer questions like: How can we explain fluctuations of national economic activity? What can economic policy do against unemployment and inflation? | |||||

Objective | This lecture will introduce the fundamentals of macroeconomic theory and explain their relevance to every-day economic problems. | |||||

Content | This course helps you understand the world in which you live. There are many questions about the macroeconomy that might spark your curiosity. Why are living standards so meagre in many African countries? Why do some countries have high rates of inflation while others have stable prices? Why have some European countries adopted a common currency? These are just a few of the questions that this course will help you answer. Furthermore, this course will give you a better understanding of the potential and limits of economic policy. As a voter, you help choose the policies that guide the allocation of society's resources. When deciding which policies to support, you may find yourself asking various questions about economics. What are the burdens associated with alternative forms of taxation? What are the effects of free trade with other countries? How does the government budget deficit affect the economy? These and similar questions are always on the minds of policy makers. | |||||

Lecture notes | The course webpage (to be found at Link) contains announcements, course information and lecture slides. | |||||

Literature | The set-up of the course will closely follow the book of N. Gregory Mankiw and Mark P. Taylor (2020), Economics, Cengage Learning, Fifth Edition. Besides this textbook, the slides, lecture notes and problem sets will cover the content of the lecture and the exam questions. |

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