Suchergebnis: Katalogdaten im Frühjahrssemester 2019

Mathematik Master Information
Wahlfächer
Für das Master-Diplom in Angewandter Mathematik ist die folgende Zusatzbedingung (nicht in myStudies ersichtlich) zu beachten: Mindestens 15 KP der erforderlichen 28 KP aus Kern- und Wahlfächern müssen aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten stammen.
Wahlfächer aus Bereichen der angewandten Mathematik ...
vollständiger Titel:
Wahlfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten
Auswahl: Finanz- und Versicherungsmathematik
NummerTitelTypECTSUmfangDozierende
401-3629-00LQuantitative Risk ManagementW4 KP2V + 1UP. Cheridito
KurzbeschreibungThis 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.
LernzielThe goal is to learn the most important methods from probability theory and statistics used in financial risk modeling.
Inhalt1. 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
SkriptCourse material is available on Link
LiteraturQuantitative Risk Management: Concepts, Techniques and Tools
AJ McNeil, R Frey and P Embrechts
Princeton University Press, Princeton, 2015 (Revised Edition)
Link
Voraussetzungen / BesonderesThe 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.
401-3923-00LSelected Topics in Life Insurance MathematicsW4 KP2VM. Koller
KurzbeschreibungStochastic 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
401-3917-00LStochastic Loss Reserving MethodsW4 KP2VR. Dahms
KurzbeschreibungLoss 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.
LernzielOur 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.
InhaltWe 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
LiteraturM. V. Wüthrich, M. Merz, Stochastic Claims Reserving Methods in Insurance, Wiley 2008.
Voraussetzungen / BesonderesThe 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 Link.

Basic knowledge in probability theory is assumed, in particular conditional expectations.
401-3956-00LEconomic Theory of Financial MarketsW4 KP2VM. V. Wüthrich
KurzbeschreibungThis lecture provides an introduction to the economic theory of financial markets. It presents the basic financial and economic concepts to insurance mathematicians and actuaries.
LernzielThis 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.
InhaltWe 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 / BesonderesThe 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.

Knowledge in probability theory, stochastic processes and statistics is assumed.
401-3936-00LData Analytics for Non-Life Insurance PricingW4 KP2VC. M. Buser, M. V. Wüthrich
KurzbeschreibungWe 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, gradient boosting machines and support vector machines.
LernzielThe student is familiar with classical actuarial pricing methods as well as with modern machine learning methods for insurance pricing and prediction.
InhaltWe 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
SkriptThe lecture notes are available from:
Link
Voraussetzungen / BesonderesThis course will be held in English and counts towards the diploma of "Aktuar SAV".
For the latter, see details under Link

Good knowledge in probability theory, stochastic processes and statistics is assumed.
401-4920-00LMarket-Consistent Actuarial Valuation
Findet dieses Semester nicht statt.
W4 KP2VM. V. Wüthrich
KurzbeschreibungIntroduction 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.
LernzielGoal 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.
InhaltIn 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)
LiteraturMarket-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).

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
Voraussetzungen / BesonderesThe 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.

Knowledge in probability theory, stochastic processes and statistics is assumed.
401-3888-00LIntroduction to Mathematical Finance Information
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.
W10 KP4V + 1UM. Larsson
KurzbeschreibungThis 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.
LernzielThis 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.
InhaltThis 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.
SkriptThe course is based on different parts from different textbooks as well as on original research literature. Lecture notes will not be available.
LiteraturLiterature:

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 / BesonderesA 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.
401-4938-14LStochastic Optimal Control Information
Findet dieses Semester nicht statt.
W4 KP2VM. Soner
KurzbeschreibungDynamic programming approach to stochastic optimal control problems will be developed. In addition to the general theory, detailed analysis of several important control problems will be given.
LernzielGoals are to achieve a deep understanding of

1. Dynamic programming approach to optimal control;
2. Several classes of important optimal control problems and their solutions.
3. To be able to use this models in engineering and economic modeling.
InhaltIn this course, we develop the dynamic programming approach for the stochastic optimal control problems. The general approach will be described and several subclasses of problems will also be discussed in including:
1. Standard exit time problems;
2. Finite and infinite horizon problems;
3. Optimal stoping problems;
4. Singular problems;
5. Impulse control problems.

After the general theory is developed, it will be applied to several classical problems including:
1. Linear quadratic regulator;
2. Merton problem for optimal investment and consumption;
3. Optimal dividend problem of (Jeanblanc and Shiryayev);
4. Finite fuel problem;
5. Utility maximization with transaction costs;
6. A deterministic differential game related to geometric flows.

Textbook will be

Controlled Markov Processes and Viscosity Solutions, 2nd edition, (W.H. Fleming and H.M. Soner) Springer-Verlag, (2005).

And lecture notes will be provided.
LiteraturControlled Markov Processes and Viscosity Solutions, 2nd edition, (W.H. Fleming and H.M. Soner) Springer-Verlag, (2005).

And lecture notes will be provided.
Voraussetzungen / BesonderesBasic knowledge of Brownian motion, stochastic differential equations and probability theory is needed.
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