Suchergebnis: Katalogdaten im Frühjahrssemester 2021

Nummer	Titel	Typ	ECTS	Umfang	Dozierende
Mathematik Bachelor
Wahlfächer
Auswahl: Finanz- und Versicherungsmathematik
401-3888-00L	Introduction to Mathematical Finance Ein verwandter Kurs ist 401-3913-01L Mathematical Foundations for Finance (3V+2U, 4 ECTS-KP). Obwohl beide Kurse unabhängig voneinander belegt werden können, darf nur einer ans gesamte Mathematik-Studium (Bachelor und Master) angerechnet werden.	W	10 KP	4V + 1U	D. Possamaï
Kurzbeschreibung	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.
Lernziel	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.
Inhalt	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.
Skript	The course is based on different parts from different textbooks as well as on original research literature. Lecture notes will not be available.
Literatur	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
Voraussetzungen / Besonderes	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.
401-3629-00L	Quantitative Risk Management	W	4 KP	2V + 1U	P. Cheridito
Kurzbeschreibung	This course introduces methods from probability theory and statistics that can be used to model financial risks. Topics addressed include loss distributions, risk measures, extreme value theory, multivariate models, copulas, dependence structures and operational risk.
Lernziel	The goal is to learn the most important methods from probability theory and statistics used in financial risk modeling.
Inhalt	1. Introduction 2. Basic Concepts in Risk Management 3. Empirical Properties of Financial Data 4. Financial Time Series 5. Extreme Value Theory 6. Multivariate Models 7. Copulas and Dependence 8. Operational Risk
Skript	Course material is available on https://people.math.ethz.ch/~patrickc/qrm
Literatur	Quantitative Risk Management: Concepts, Techniques and Tools AJ McNeil, R Frey and P Embrechts Princeton University Press, Princeton, 2015 (Revised Edition) http://press.princeton.edu/titles/10496.html
Voraussetzungen / Besonderes	The course corresponds to the Risk Management requirement for the SAA ("Aktuar SAV Ausbildung") as well as for the Master of Science UZH-ETH in Quantitative Finance.
401-3923-00L	Selected Topics in Life Insurance Mathematics	W	4 KP	2V	M. Koller
Kurzbeschreibung	Stochastic Models for Life insurance 1) Markov chains 2) Stochastic Processes for demography and interest rates 3) Cash flow streams and reserves 4) Mathematical Reserves and Thiele's differential equation 5) Theorem of Hattendorff 6) Unit linked policies
Lernziel
401-3917-00L	Stochastic Loss Reserving Methods	W	4 KP	2V	R. Dahms
Kurzbeschreibung	Loss Reserving is one of the central topics in non-life insurance. Mathematicians and actuaries need to estimate adequate reserves for liabilities caused by claims. These claims reserves have influence all financial statements, future premiums and solvency margins. We present the stochastics behind various methods that are used in practice to calculate those loss reserves.
Lernziel	Our goal is to present the stochastics behind various methods that are used in prctice to estimate claim reserves. These methods enable us to set adequate reserves for liabilities caused by claims and to determine prediction errors of these predictions.
Inhalt	We will present the following stochastic claims reserving methods/models: - Stochastic Chain-Ladder Method - Bayesian Methods, Bornhuetter-Ferguson Method, Credibility Methods - Distributional Models - Linear Stochastic Reserving Models, with and without inflation - Bootstrap Methods - Claims Development Result (solvency view) - Coupling of portfolios
Literatur	M. V. Wüthrich, M. Merz, Stochastic Claims Reserving Methods in Insurance, Wiley 2008.
Voraussetzungen / Besonderes	The exams ONLY take place during the official ETH examination periods. This course will be held in English and counts towards the diploma "Aktuar SAV". For the latter, see details under www.actuaries.ch. Basic knowledge in probability theory is assumed, in particular conditional expectations.
401-3956-00L	Economic Theory of Financial Markets	W	4 KP	2V	M. V. Wüthrich
Kurzbeschreibung	This lecture provides an introduction to the economic theory of financial markets. It presents the basic financial and economic concepts to insurance mathematicians and actuaries.
Lernziel	This lecture aims at providing the fundamental financial and economic concepts to insurance mathematicians and actuaries. It focuses on portfolio theory, cash flow valuation and deflator techniques.
Inhalt	We treat the following topics: - Fundamental concepts in economics - Portfolio theory - Mean variance analysis, capital asset pricing model - Arbitrage pricing theory - Cash flow theory - Valuation principles - Stochastic discounting, deflator techniques - Interest rate modeling - Utility theory
Voraussetzungen / Besonderes	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 www.actuaries.ch. Knowledge in probability theory, stochastic processes and statistics is assumed.
401-3936-00L	Data Analytics for Non-Life Insurance Pricing	W	4 KP	2V	C. M. Buser, M. V. Wüthrich
Kurzbeschreibung	We study statistical methods in supervised learning for non-life insurance pricing such as generalized linear models, generalized additive models, Bayesian models, neural networks, classification and regression trees, random forests and gradient boosting machines.
Lernziel	The student is familiar with classical actuarial pricing methods as well as with modern machine learning methods for insurance pricing and prediction.
Inhalt	We present the following chapters: - generalized linear models (GLMs) - generalized additive models (GAMs) - neural networks - credibility theory - classification and regression trees (CARTs) - bagging, random forests and boosting
Skript	The lecture notes are available from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2870308
Voraussetzungen / Besonderes	This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under www.actuaries.ch Good knowledge in probability theory, stochastic processes and statistics is assumed.
401-4920-00L	Market-Consistent Actuarial Valuation Findet dieses Semester nicht statt.	W	4 KP	2V	M. V. Wüthrich
Kurzbeschreibung	Introduction to market-consistent actuarial valuation. Topics: Stochastic discounting, full balance sheet approach, valuation portfolio in life and non-life insurance, technical and financial risks, risk management for insurance companies.
Lernziel	Goal is to give the basic mathematical tools for describing insurance products within a financial market and economic environment and provide the basics of solvency considerations.
Inhalt	In this lecture we give a full balance sheet approach to the task of actuarial valuation of an insurance company. Therefore we introduce a multidimensional valuation portfolio (VaPo) on the liability side of the balance sheet. The basis of this multidimensional VaPo is a set of financial instruments. This approach makes the liability side of the balance sheet directly comparable to its asset side. The lecture is based on four sections: 1) Stochastic discounting 2) Construction of a multidimensional Valuation Portfolio for life insurance products (with guarantees) 3) Construction of a multidimensional Valuation Portfolio for a run-off portfolio of a non-life insurance company 4) Measuring financial risks in a full balance sheet approach (ALM risks)
Literatur	Market-Consistent Actuarial Valuation, 3rd edition. Wüthrich, M.V. EAA Series, Springer 2016. ISBN: 978-3-319-46635-4 Wüthrich, M.V., Merz, M. Claims run-off uncertainty: the full picture. SSRN Manuscript ID 2524352 (2015). England, P.D, Verrall, R.J., Wüthrich, M.V. On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins. Insurance: Mathematics and Economics 85 (2019), 74-88. Wüthrich, M.V., Embrechts, P., Tsanakas, A. Risk margin for a non-life insurance run-off. Statistics & Risk Modeling 28 (2011), no. 4, 299--317. Financial Modeling, Actuarial Valuation and Solvency in Insurance. Wüthrich, M.V., Merz, M. Springer Finance 2013. ISBN: 978-3-642-31391-2 Cheridito, P., Ery, J., Wüthrich, M.V. Assessing asset-liability risk with neural networks. Risks 8/1 (2020), article 16.
Voraussetzungen / Besonderes	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 www.actuaries.ch. Knowledge in probability theory, stochastic processes and statistics is assumed.

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