Suchergebnis: Katalogdaten im Frühjahrssemester 2017

Mathematik Bachelor Information
Bachelor-Studium (Studienreglement 2010)
Wahlfächer
Auswahl: Algebra, Topologie, diskrete Mathematik, Logik
NummerTitelTypECTSUmfangDozierende
401-3106-17LClass Field TheoryW6 KP2V + 1UJ. Fresán
KurzbeschreibungClass Field Theory aims at describing the Galois group of the maximal abelian extension of global and local fields.
Lernziel
Literatur[1] D. Harari, Cohomologie galoisienne et théorie du corps de classes, EDP Sciences, CNRS Éditions, Paris, 2017.
[2] K. Kato, N. Kurokawa, T. Saito, Number theory 2. Introduction to class field theory, Translations of Mathematical Monographs 240, AMS, 2011.
[3] J. S. Milne, Class Field Theory (available at http://www.jmilne.org/math/CourseNotes/cft.html)
[4] J-P. Serre, Local fields, Grad. Texts Math. 67. Springer-Verlag, 1979.
401-3058-00LKombinatorik IW4 KP2GN. Hungerbühler
KurzbeschreibungDer Kurs Kombinatorik I und II ist eine Einfuehrung in die abzaehlende Kombinatorik.
LernzielDie Studierenden sind in der Lage, kombinatorische Probleme einzuordnen und die adaequaten Techniken zu deren Loesung anzuwenden.
InhaltInhalt der Vorlesungen Kombinatorik I und II: Kongruenztransformationen der Ebene, Symmetriegruppen von geometrischen Figuren, Eulersche Funktion, Cayley-Graphen, formale Potenzreihen, Permutationsgruppen, Zyklen, Lemma von Burnside, Zyklenzeiger, Saetze von Polya, Anwendung auf die Graphentheorie und isomere Molekuele.
Voraussetzungen / BesonderesWer 401-3052-00L Kombinatorik (letztmals im FS 2008 gelesen) für den Bachelor- oder Master-Studiengang Mathematik anrechnen lässt, darf 401-3058-00L Kombinatorik I nur noch fürs Mathematik Lehrdiplom oder fürs Didaktik-Zertifikat Mathematik anrechnen lassen.
401-3112-17LIntroduction to Number TheoryW4 KP2VC. Busch
KurzbeschreibungThis course gives an introduction to number theory. The focus will be on algebraic number theory.
Lernziel
InhaltThe following subjects will be covered:
- Euclidean algorithm, greatest common divisor, ...
- Congruences, Chinese Remainder Theorem
- Quadratic residues, Legendre symbol, law of quadratic reciprocity
- Quadratic number fields, integers and primes
- Units of quadratic number fields, Pell's equation, Dirichlet unit theorem
- Continued fractions and quadratic irrationalities, Theorem of Euler Lagrange, relation to units.
Literatur- A. Fröhlich, M.J. Taylor, Algebraic number theory, Cambridge studies in advanced mathematics 27, Cambridge University Press, 1991
- S. Lang, Algebraic Number Theory, Second Edition, Graduate Texts in Mathematics, 110, Springer, 1994
- J. Neukirch, Algebraic number theory, Grundlehren der mathematischen Wissenschaften 322, Springer 1999
- R. Remmert, P. Ullrich, Elementare Zahlentheorie, Grundstudium Mathematik, Basel Birkhäuser, 2008
- P. Samuel, Algebraic Theory of Numbers, Kershaw Publishing Company LTD, 1972 (Original edition in French at Hermann)
- J.-P. Serre, A Course in Arithmetic, Graduate Texts in Mathematics 7, Springer 1973 (Original edition in French at Presses Universitaires de France)
Voraussetzungen / BesonderesBasic knowledge of Algebra as taught in a course Algebra I + II.
Auswahl: Geometrie
NummerTitelTypECTSUmfangDozierende
401-4206-17LGroup Actions on TreesW4 KP2VN. Lazarovich
KurzbeschreibungAs a main theme, we will explain how an action of a group on a tree enables us to break the group into smaller pieces, and thus gain better understanding of its structure. After introducing the general theory, we will cover various topics in this general theme.
LernzielIntroduction to the general theory of group actions on trees, also known as Bass-Serre theory, and various important results on decompositions of groups.
InhaltDepending on time we will cover some of the following topics.
- Free groups and their subgroups.
- The general theory of actions on trees, i.e, Bass-Serre theory.
- Trees as 1-dimensional buildings.
- Stallings' theorem.
- Grushko's and Dunwoody's accessibility results.
- Actions on R-trees and the Rips machine.
LiteraturJ.-P. Serre, Trees. (Translated from the French by John Stillwell). Springer-Verlag, 1980. ISBN 3-540-10103-9

C. T. C. Wall. The geometry of abstract groups and their splittings. Revista Matemática Complutense vol. 16(2003), no. 1, pp. 5-101
Voraussetzungen / BesonderesFamiliarity with the basics of fundamental group (and covering theory).
401-4148-17LReading Course: Introduction to the Moduli of Maps and Gromow-Witten InvariantsW2 KP4AG. Bérczi
KurzbeschreibungEnumerative questions motivated the development of algebraic geometry for centuries. This course is a short tour to some ideas which have revolutionised enumerative geometry in the last 30 years: stable maps, Gromov-Witten invariants and quantum cohomology.
LernzielThe aim of the course is to understand the concept of stable maps, their moduli and quantum cohomology. We prove Kontsevich's celebrated formula on the number of plane rational curves of degree d passing through 3d-1 given points in general position.
InhaltTopics covered:
1) Brief survey on moduli spaces: fine and coarse moduli.
2) Stable n-pointed curves
3) Stable maps
4) Enumerative geometry via stable maps
5) Gromov-Witten invariants
6) Quantum cohomology and quantum product
7) Kontsevich's formula
LiteraturThe main reference for the course is:
J. Kock and I.Vainsencher: Kontsevich's Formula for Rational Plane Curves
www.math.utah.edu/%7eyplee/teaching/gw/Koch.pdf

Background material:
-Algebraic varieties: I. R. Shafarevich, Basic Algebraic geometry 1 & 2, Springer-Verlag.
-Moduli of curves: Joe Harris and Ian Morrison, Moduli of Curves, Graduate Texts in Mathematics 187, Springer-Verlag
-Moduli spaces (fine and coarse): Peter. E. Newstead, Introduction to Moduli Problems and Orbit Spaces, Tata Institute Lecture Notes, Springer-Verlag
Voraussetzungen / BesonderesSome minimal background in algebraic geometry (varieties, line bundles, Grassmannians, curves).
Basic concepts of moduli spaces (fine and coarse) and group actions will be explained mainly through examples.
401-3056-00LEndliche Geometrien I
Findet dieses Semester nicht statt.
W4 KP2GN. Hungerbühler
KurzbeschreibungEndliche Geometrien I, II: Endliche Geometrien verbinden Aspekte der Geometrie mit solchen der diskreten Mathematik und der Algebra endlicher Körper. Inbesondere werden Modelle der Inzidenzaxiome konstruiert und Schliessungssätze der Geometrie untersucht. Anwendungen liegen im Bereich der Statistik, der Theorie der Blockpläne und der Konstruktion orthogonaler lateinischer Quadrate.
LernzielEndliche Geometrien I, II: Die Studierenden sind in der Lage, Modelle endlicher Geometrien zu konstruieren und zu analysieren. Sie kennen die Schliessungssätze der Inzidenzgeometrie und können mit Hilfe der Theorie statistische Tests entwerfen sowie orthogonale lateinische Quadrate konstruieren. Sie sind vertraut mit Elementen der Theorie der Blockpläne.
InhaltEndliche Geometrien I, II: Endliche Körper, Polynomringe, endliche affine Ebenen, Axiome der Inzidenzgeometrie, Eulersches Offiziersproblem, statistische Versuchsplanung, orthogonale lateinische Quadrate, Transformationen endlicher Ebenen, Schliessungsfiguren von Desargues und Pappus-Pascal, Hierarchie der Schliessungsfiguren, endliche Koordinatenebenen, Schiefkörper, endliche projektive Ebenen, Dualitätsprinzip, endliche Möbiusebenen, selbstkorrigierende Codes, Blockpläne
Literatur- Max Jeger, Endliche Geometrien, ETH Skript 1988

- Albrecht Beutelspacher: Einführung in die endliche Geometrie I,II. Bibliographisches Institut 1983

- Margaret Lynn Batten: Combinatorics of Finite Geometries. Cambridge University Press

- Dembowski: Finite Geometries.
401-3574-61LIntroduction to Knot Theory Information
Findet dieses Semester nicht statt.
W6 KP3G
KurzbeschreibungIntroduction to the mathematical theory of knots. We will discuss some elementary topics in knot theory and we will repeatedly centre on how this knowledge can be used in secondary school.
LernzielThe aim of this lecture course is to give an introduction to knot theory. In the course we will discuss the definition of a knot and what is meant by equivalence. The focus of the course will be on knot invariants. We will consider various knot invariants amongst which we will also find the so called knot polynomials. In doing so we will again and again show how this knowledge can be transferred down to secondary school.
InhaltDefinition of a knot and of equivalent knots.
Definition of a knot invariant and some elementary examples.
Various operations on knots.
Knot polynomials (Jones, ev. Alexander.....)
LiteraturAn extensive bibliography will be handed out in the course.
Voraussetzungen / BesonderesPrerequisites are some elementary knowledge of algebra and topology.
Auswahl: Analysis
NummerTitelTypECTSUmfangDozierende
401-3352-09LAn Introduction to Partial Differential EquationsW6 KP3VF. Da Lio
KurzbeschreibungThis course aims at being an introduction to first and second order partial differential equations (in short PDEs).
We will present the so called method of characteristics to solve quasilinear PDEs and some basic properties of classical solutions to second order linear PDEs.
Lernziel
InhaltA preliminary plan is the following
- Laplace equation, fundamental solution, harmonic functions and main properties, maximum principle. Poisson equation. Green functions. Perron method for the solution of the Dirichlet problem.
- Weak and strong maximum principle for elliptic operators.
- Heat equation, fundamental solution, existence of solutions to the Cauchy problem and representation formulas, main properties, uniqueness by maximum principle, regularity.
- Wave equation, existence of the solution, D'Alembert formula, solutions by spherical means, main properties, uniqueness by energy methods.
- The Method of characteristics for first order equations, linear and nonlinear, transport equation, Hamilton-Jacobi equation, scalar conservation laws.
- A brief introduction to viscosity solutions.
SkriptThe teacher provides the students with personal notes.
LiteraturBibliography
- L.Evans Partial Differential Equations, AMS 2010 (2nd edition)
- D. Gilbarg, N.S. Trudinger Elliptic Partial Differential Equations of Second Order, Springer, 1998.
- E. Di Benedetto Partial Differential Equations, Birkauser, 2010 (2nd edition).
- W. A. Strauss Partial Differential Equations. An Introduction, Wiley, 1992.
Voraussetzungen / BesonderesDifferential and integral calculus for functions of several variables; elementary theory of ordinary differential equations, basic facts of measure theory.
401-3496-17LTopics in the Calculus of VariationsW4 KP2VA. Figalli
Kurzbeschreibung
Lernziel
Auswahl: Numerische Mathematik
NummerTitelTypECTSUmfangDozierende
252-0504-00LNumerical Methods for Solving Large Scale Eigenvalue Problems Information
Findet dieses Semester nicht statt.
W4 KP3GP. Arbenz
KurzbeschreibungDie Vorlesung behandelt Algorithmen zur Lösung von Eigenwertproblemen
mit grossen, schwach besetzten Matrizen. Die z.T. erst in den letzten Jahren
entwickelten Verfahren werden theoretisch und praktisch mit MATLAB
untersucht.
LernzielKenntnisse der modernen Eigenlöser, ihres numerischen Verhaltens, ihrer Einsatzmöglichkeiten und Grenzen.
InhaltDie Vorlesung beginnt mit verschiedenartigen Beispielen für Anwendungen
in denen Eigenwertprobleme eine wichtige Rolle spielen. Nach einer
Einführung in die Lineare Algebra der Eigenwertprobleme wird ein
Überblick über Verfahren (QR-Algorithmus u.ä.) zur Behandlung kleiner
und mittelgrosser Eigenwertprobleme gegeben.

Danach werden die heute wichtigsten Löser für grosse, typischerweise
schwach-besetzte Matrixeigenwertprobleme vorgestellt und analysiert.
Dabei wird eine Auswahl der folgenden Themen behandelt:

* Vektor- und Teilraumiteration
* Spurminimierungsalgorithmus
* Arnoldi- und Lanczos-Algorithmus (inkl. Varianten mit Neustart)
* Davidson- und Jacobi-Davidson-Algorithmus
* vorkonditionierte inverse Iteration und LOBPCG
* Verfahren für nichtlineaere Eigenwertprobleme

In den Übungen werden diese Algorithmen (in vereinfachter Form) in
MATLAB implementiert und numerisch untersucht.
SkriptLecture notes (Englisch),
Kopien der Folien
LiteraturZ. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst: Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM, Philadelphia, 2000.

Y. Saad: Numerical Methods for Large Eigenvalue Problems. Manchester University Press, Manchester, 1994.

G. H. Golub and Ch. van Loan: Matrix Computations, 3rd ed. Johns Hopkins University Press, Baltimore 1996.
Voraussetzungen / BesonderesVoraussetzung: Lineare Algebra
Auswahl: Wahrscheinlichkeitstheorie, Statistik
NummerTitelTypECTSUmfangDozierende
401-3919-60LAn Introduction to the Modelling of ExtremesW4 KP2VP. Embrechts
KurzbeschreibungThis course yields an introduction into the MATHEMATICAL THEORY of one-dimensional extremes, and this mainly from a more probabilistic point of view.
LernzielIn this course, students learn to distinguish between so-called normal models, i.e. models based on the normal or Gaussian distribution, and so-called heavy-tailed or power-tail models.
They learn to do probabilistic modelling of extremes in one-dimensional data. The probabilistic key theorems are the Fisher-Tippett Theorem and the Balkema-de Haan-Pickands Theorem. These lead to the statistical techniques for the analysis of extremes or rare events known as the Block Method, and Peaks Over Threshold method, respectively.
Inhalt- Introduction to rare or extreme events
- Regular Variation
- The Convergence to Types Theorem
- The Fisher-Tippett Theorem
- The Method of Block Maxima
- The Maximal Domain of Attraction
- The Fre'chet, Gumbel and Weibull distributions
- The POT method
- The Point Process Method: a first introduction
- The Pickands-Balkema-de Haan Theorem and its applications
- Some extensions and outlook
SkriptThere will be no script available, students are required to take notes from the blackboard lectures. The course follows closely Extreme Value Theory as developed in:
P. Embrechts, C. Klueppelberg and T. Mikosch (1997)
Modelling Extremal Events for Insurance and Finance.
Springer.
LiteraturThe main text on which the course is based is:
P. Embrechts, C. Klueppelberg and T. Mikosch (1997)
Modelling Extremal Events for Insurance and Finance.
Springer.
Further relevant literature is:
S. I. Resnick (2007) Heavy-Tail Phenomena. Probabilistic and
Statistical Modeling. Springer.
S. I. Resnick (1987) Extreme Values, Regular Variation,
and Point Processes. Springer.
401-6102-00LMultivariate StatisticsW4 KP2GN. Meinshausen
KurzbeschreibungMultivariate Statistics deals with joint distributions of several random variables. This course introduces the basic concepts and provides an overview over classical and modern methods of multivariate statistics. We will consider the theory behind the methods as well as their applications.
LernzielAfter the course, you should be able to:
- describe the various methods and the concepts and theory behind them
- identify adequate methods for a given statistical problem
- use the statistical software "R" to efficiently apply these methods
- interpret the output of these methods
InhaltVisualization / Principal component analysis / Multidimensional scaling / The multivariate Normal distribution / Factor analysis / Supervised learning / Cluster analysis
SkriptNone
LiteraturThe course will be based on class notes and books that are available electronically via the ETH library.
Voraussetzungen / BesonderesTarget audience: This course is the more theoretical version of "Applied Multivariate Statistics" (401-0102-00L) and is targeted at students with a math background.

Prerequisite: A basic course in probability and statistics.

Note: The courses 401-0102-00L and 401-6102-00L are mutually exclusive. You may register for at most one of these two course units.
401-3822-17LPercolation and Ising ModelW4 KP2VV. Tassion
KurzbeschreibungIn this course we will provide a general introduction to the Ising model on the hypercubic lattice Z^d (main properties, standard mathematical tools).
In order to answer important questions regarding the Ising model, we will exploit a deep connection of the model with two (dependent) percolation processes, the Fortuin-Kastelen percolation and the random-current model.
Lernziel- Discover important models of statistical mechanics: the Ising model (and its random current representation) and FK percolation.
- Learn some important techniques in statistical mechanics (e.g. coupling methods, monotonicity properties, the use of differential inequalities, to name few).
Voraussetzungen / Besonderes- Probability Theory.
- The course "Recent Development in Percolation Theory" (Autumn 2017) of Pierre Nolin is advised but not necessary (the overlap with Nolin's course will be minimal).
401-3616-17LAn Introduction to Stochastic Partial Differential EquationsW8 KP4GA. Jentzen
KurzbeschreibungIn this course solutions of semilinear stochastic partial differential equations (SPDEs) of the evolutionary type are investigated. Semilinear SPDEs are a key ingredient in a number of models from economics and the natural sciences.
LernzielThe aim of this course is to teach the students a decent knowledge on solutions of semilinear stochastic partial differential equations (SPDEs) and on the functional analytic and probabilistic concepts used to formulate and study such equations.
InhaltThe course includes content (i) on the (functional) analytic concepts used to study semilinear stochastic partial differential equations (SPDEs), (ii) on the probabilistic concepts used to study SPDEs, and (iii) on solutions of SPDEs (e.g., existence, uniqueness and regularity properties of mild solutions of SPDEs, applications involving SPDEs). Semilinear SPDEs are a key ingredient in a number of models from economics and the natural sciences. They appear, for example, in models from neurobiology for the approximative description of the propagation of electrical impulses along nerve cells, in models from financial engineering for the approximative pricing of financial derivatives, in models from fluid mechanics for the approximative description of velocity fields in fully developed turbulent flows, in models from quantum field theory for describing the temporal dynamics associated to Euclidean quantum field theories, and in models from chemistry for the approximative description of the temporal evolution of the concentration of an undesired chemical contaminant in the groundwater system.
SkriptThe current version of the lecture notes is available as a PDF file here:
https://polybox.ethz.ch/index.php/s/bI884u6tz9mO9Vz/download
Literatur1. Stochastic Equations in Infinite Dimensions
G. Da Prato and J. Zabczyk
Cambridge Univ. Press (1992)

2. Taylor Approximations for Stochastic Partial Differential Equations
A. Jentzen and P.E. Kloeden
Siam (2011)

3. Numerical Solution of Stochastic Differential Equations
P.E. Kloeden and E. Platen
Springer Verlag (1992)

4. A Concise Course on Stochastic Partial Differential Equations
C. Prévôt and M. Röckner
Springer Verlag (2007)

5. Galerkin Finite Element Methods for Parabolic Problems
V. Thomée
Springer Verlag (2006)
Voraussetzungen / BesonderesMandatory prerequisites: Functional analysis, probability theory;
Recommended prerequisites: stochastic processes;
Auswahl: Finanz- und Versicherungsmathematik
NummerTitelTypECTSUmfangDozierende
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 + 1UJ. Teichmann
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 and presumes a knowledge of measure-theoretic probability theory (as taught e.g. in the course "Probability Theory"). The course will be offered every year in the Spring semester. The textbook by Föllmer and Schied or lecture notes similar to that will be used.

This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MFII), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MFI, is taken prior to MFII.
SkriptThe textbook by Föllmer and Schied or lecture notes similar to that will be used. However, actual lecture notes will not be available.
LiteraturRecommended textbook:

Hans Föllmer and Alexander Schied, "Stochastic Finance: An Introduction in Discrete Time", de Gruyter
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" (MFII), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MFI, is taken prior to MFII.
401-3629-00LQuantitative Risk Management Information W4 KP2VP. Cheridito
KurzbeschreibungThis course introduces methods from probability theory and statistics that can be used to model financial risks. Topics addressed include loss distributions, multivariate models, copulas and dependence structures, extreme value theory, risk measures, aggregation of risk, and risk allocation.
LernzielThe goal is to learn the most important methods from probability theory and statistics used to model financial risks.
Inhalt1. Risk in Perspective
2. Basic Concepts
3. Multivariate Models
4. Copulas and Dependence
5. Aggregate Risk
6. Extreme Value Theory
7. Operational Risk and Insurance Analytics
SkriptCourse material is available on https://people.math.ethz.ch/~patrickc/qrm
LiteraturQuantitative 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 / 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 www.actuaries.ch.

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 www.actuaries.ch.

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, 2nd edition.
Wüthrich, M.V., Bühlmann, H., Furrer, H.
EAA Series Textbook, Springer, 2010.
ISBN: 978-3-642-14851-4

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 www.actuaries.ch.

Knowledge in probability theory, stochastic processes and statistics is assumed.
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