Suchergebnis: Katalogdaten im Frühjahrssemester 2020
Mathematik Bachelor | ||||||
Kernfächer | ||||||
Kernfächer aus Bereichen der angewandten Mathematik ... vollständiger Titel: Kernfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|---|
401-3632-00L | Computational Statistics | W | 8 KP | 3V + 1U | M. H. Maathuis | |
Kurzbeschreibung | We discuss modern statistical methods for data analysis, including methods for data exploration, prediction and inference. We pay attention to algorithmic aspects, theoretical properties and practical considerations. The class is hands-on and methods are applied using the statistical programming language R. | |||||
Lernziel | The student obtains an overview of modern statistical methods for data analysis, including their algorithmic aspects and theoretical properties. The methods are applied using the statistical programming language R. | |||||
Voraussetzungen / Besonderes | At least one semester of (basic) probability and statistics. Programming experience is helpful but not required. | |||||
401-3602-00L | Applied Stochastic Processes Findet dieses Semester nicht statt. | W | 8 KP | 3V + 1U | keine Angaben | |
Kurzbeschreibung | Poisson-Prozesse; Erneuerungsprozesse; Markovketten in diskreter und in stetiger Zeit; einige Beispiele und Anwendungen. | |||||
Lernziel | Stochastische Prozesse dienen zur Beschreibung der Entwicklung von Systemen, die sich in einer zufälligen Weise entwickeln. In dieser Vorlesung bezieht sich die Entwicklung auf einen skalaren Parameter, der als Zeit interpretiert wird, so dass wir die zeitliche Entwicklung des Systems studieren. Die Vorlesung präsentiert mehrere Klassen von stochastischen Prozessen, untersucht ihre Eigenschaften und ihr Verhalten und zeigt anhand von einigen Beispielen, wie diese Prozesse eingesetzt werden können. Die Hauptbetonung liegt auf der Theorie; "applied" ist also im Sinne von "applicable" zu verstehen. | |||||
Literatur | R. N. Bhattacharya and E. C. Waymire, "Stochastic Processes with Applications", SIAM (2009), available online: Link R. Durrett, "Essentials of Stochastic Processes", Springer (2012), available online: Link M. Lefebvre, "Applied Stochastic Processes", Springer (2007), available online: Link S. I. Resnick, "Adventures in Stochastic Processes", Birkhäuser (2005) | |||||
Voraussetzungen / Besonderes | Prerequisites are familiarity with (measure-theoretic) probability theory as it is treated in the course "Probability Theory" (401-3601-00L). | |||||
401-3652-00L | Numerical Methods for Hyperbolic Partial Differential Equations (University of Zurich) Der Kurs muss direkt an der UZH belegt werden. UZH Modulkürzel: MAT827 Beachten Sie die Einschreibungstermine an der UZH: Link | W | 10 KP | 4V + 2U | Uni-Dozierende | |
Kurzbeschreibung | This course treats numerical methods for hyperbolic initial-boundary value problems, ranging from wave equations to the equations of gas dynamics. The principal methods discussed in the course are finite volume methods, including TVD, ENO and WENO schemes. Exercises involve implementation of numerical methods in MATLAB. | |||||
Lernziel | The goal of this course is familiarity with the fundamental ideas and mathematical consideration underlying modern numerical methods for conservation laws and wave equations. | |||||
Inhalt | * Introduction to hyperbolic problems: Conservation, flux modeling, examples and significance in physics and engineering. * Linear Advection equations in one dimension: Characteristics, energy estimates, upwind schemes. * Scalar conservation laws: shocks, rarefactions, solutions of the Riemann problem, weak and entropy solutions, some existence and uniqueness results, finite volume schemes of the Godunov, Engquist-Osher and Lax-Friedrichs type. Convergence for monotone methods and E-schemes. * Second-order schemes: Lax-Wendroff, TVD schemes, limiters, strong stability preserving Runge-Kutta methods. * Linear systems: explicit solutions, energy estimates, first- and high-order finite volume schemes. * Non-linear Systems: Hugoniot Locus and integral curves, explicit Riemann solutions of shallow-water and Euler equations. Review of available theory. | |||||
Skript | Lecture slides will be made available to participants. However, additional material might be covered in the course. | |||||
Literatur | H. Holden and N. H. Risebro, Front Tracking for Hyperbolic Conservation Laws, Springer 2011. Available online. R. J. LeVeque, Finite Volume methods for hyperbolic problems, Cambridge university Press, 2002. Available online. E. Godlewski and P. A. Raviart, Hyperbolic systems of conservation laws, Ellipses, Paris, 1991. | |||||
Voraussetzungen / Besonderes | Having attended the course on the numerical treatment of elliptic and parabolic problems is no prerequisite. Programming exercises in MATLAB Former course title: "Numerical Solution of Hyperbolic Partial Differential Equations" | |||||
» Kernfächer aus Bereichen der angewandten Mathematik ... (Mathematik Master) | ||||||
Kernfächer aus weiteren anwendungsorientierten Gebieten 402-0204-00L Elektrodynamik ist als angewandtes Kernfach im Bachelor-Studiengang Mathematik anrechenbar, aber nur unter der Bedingung, dass 402-0224-00L Theoretische Physik (letztmals im FS 2016 angeboten) nicht angerechnet wird (weder im Bachelor- noch im Master-Studiengang). Wenden Sie sich für die Kategoriezuordnung nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (Link). | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
402-0204-00L | Elektrodynamik | W | 7 KP | 4V + 2U | R. Renner | |
Kurzbeschreibung | Herleitung und Diskussion der Maxwellgleichungen, vom statischen Fall zur Elektrodynamik. Wellengleichung, Wellenleiter, Kavitäten. Erzeugung elektromagnetischer Strahlung, Streuung und Beugung von Licht. Struktur der Maxwellgleichungen, Lorentz-Invarianz, Relativitätstheorie und Kovarianz, Lagrange Formulierung. Dynamik relativistischer Teilchen im Feld und deren Strahlung. | |||||
Lernziel | Physikalisches Verständnis statischer und dynamischer Phänomene (bewegter) geladener Objekte, und der Struktur der klassischen Feldtheorie der Elektrodynamik (transversale versus longitudinale Physik, Invarianzen (Lorentz-, Eich-)). Erkennen des Zusammenhangs von elektrischen, magnetischen und optischen Phänomenen und Einfluss von Medien. Verständnis klassischer Phänomene der Elektrodynamik und Fähigkeit zur selbständigen Lösung einfacher Probleme. Anwendung mathematischer Fertigkeiten (Vektoranalysis, vollständige Funktionensysteme, Green'sche Funktionen, ko- und kontravariante Koordinaten, etc.). Vorbereitung auf die Quantenmechanik (Eigenwertprobleme, Lichtleiter und Kavitäten). | |||||
Inhalt | Klassische Feldtheorie der Elektrodynamik: Herleitung und Diskussion der Maxwellgleichungen, ausgehend vom statischen Fall (Elektrostatik, Magnetostatik, Randwertprobleme) im Vakuum und in Medien und Verallgemeinerung zur Elektrodynamik (Faraday Gesetz, Ampere/Maxwell; Potentiale, Eichinvarianz). Wellengleichung und Lösungen im vollen Raum, Halbraum (Snellius Gesetz), Wellenleiter, Kavitäten. Erzeugung elektromagnetischer Strahlung, Streuung und Beugung von Licht (Optik). Erarbeitung von Beispielen. Diskussion zur Struktur der Maxwellgleichungen, Lorentz-Invarianz, Relativitätstheorie und Kovarianz, Lagrange Formulierung. Dynamik relativistischer Teilchen im Feld und deren Strahlung (Synchrotron). | |||||
Literatur | J.D. Jackson, Classical Electrodynamics W.K.H Panovsky and M. Phillis, Classical electricity and magnetism L.D. Landau, E.M. Lifshitz, and L.P. Pitaevskii, Electrodynamics of continuus media A. Sommerfeld, Elektrodynamik, Optik (Vorlesungen über theoretische Physik) M. Born and E. Wolf, Principles of optics R. Feynman, R. Leighton, and M. Sands, The Feynman Lectures of Physics, Vol II W. Nolting, Elektrodynamik (Grundkurs Theoretische Physik 3) | |||||
Wahlfächer | ||||||
Auswahl: Algebra, Zahlentheorie, Topologie, diskrete Mathematik, Logik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3201-00L | Algebraic Groups | W | 8 KP | 4G | P. D. Nelson | |
Kurzbeschreibung | Introduction to the theory of linear algebraic groups. Lie algebras, the Jordan Chevalley decomposition, semisimple and reductive groups, root systems, Borel subgroups, classification of reductive groups and their representations. | |||||
Lernziel | ||||||
Literatur | A. L. Onishchik and E.B. Vinberg, Lie Groups and Algebraic Groups | |||||
Voraussetzungen / Besonderes | Abstract algebra: groups, rings, fields, tensor product, etc. Some familiarity with the basics of Lie groups and their Lie algebras would be helpful, but is not absolutely necessary. We will develop what we need from algebraic geometry, without assuming prior knowledge. | |||||
401-3109-65L | Probabilistic Number Theory Findet dieses Semester nicht statt. | W | 8 KP | 4G | E. Kowalski | |
Kurzbeschreibung | The course presents some results of probabilistic number theory in a unified manner, including distribution properties of the number of prime divisors of integers, probabilistic properties of the zeta function and statistical distribution of exponential sums. | |||||
Lernziel | The goal of the course is to present some results of probabilistic number theory in a unified manner. | |||||
Inhalt | The main concepts will be presented in parallel with the proof of a few main theorems: (1) the Erdős-Wintner and Erdős-Kac theorems concerning the distribution of values of arithmetic functions; (2) the distribution of values of the Riemann zeta function, including Selberg's central limit theorem for the Riemann zeta function on the critical line; (3) the Chebychev bias for primes in arithmetic progressions; (4) functional limit theorems for the paths of partial sums of families of exponential sums. | |||||
Skript | The lecture notes for the class are available at Link | |||||
Voraussetzungen / Besonderes | Prerequisites: Complex analysis, measure and integral; some probability theory is useful but the main concepts needed will be recalled. Some knowledge of number theory is useful but the main results will be summarized. | |||||
401-3202-09L | The Representation Theory of the Finite Symmetric Groups NOTICE: No physical class for the next few weeks until further notice. Instead a video recording will be offered. | W | 4 KP | 2V | L. Wu | |
Kurzbeschreibung | This course is an Introduction to the Representation Theory of the Groups. | |||||
Lernziel | Our goal is to give an introduction of the Representation Theory using the examples of the Finite Symmetry Groups. | |||||
Literatur | * Jean-Pierre Serre: Linear Representations of Finite Groups, Graduate Texts in Mathematics, Springer. * William Fulton and Joe Harris: Representation Theory A First Course, Graduate Texts in Mathematics, Springer. * G. D. James: The Representation Theory of the Symmetric Groups, Lecture Notes in Mathematics, Springer. * Bruce E. Sagan: The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Graduate Texts in Mathematics, Springer. | |||||
Voraussetzungen / Besonderes | Some basic knowledge of the Group Theory and Linear Algebra. | |||||
401-8112-20L | Geometry of Numbers (University of Zurich) Der Kurs muss direkt an der UZH belegt werden. UZH Modulkürzel: MAT548 Beachten Sie die Einschreibungstermine an der UZH: Link | W | 9 KP | 4V + 1U | Uni-Dozierende | |
Kurzbeschreibung | The Geometry of Numbers studies distribution of lattice points in the n dimensional space, for instance, existence of lattice points in various domains and existence of integral solutions of polynomial inequalities. This subject is also closely related to the Theory of Diophantine Approximation, which seeks good rational approximations for real vectors. | |||||
Lernziel | Learn basic techniques in the Geometry of Numbers | |||||
Literatur | 1. Cassels, An introduction to Diophantine Approximation 2. Cassels, An introduction to the Geometry of Numbers 3. Schmidt, Diophantine approximation 4. Siegel, Lectures on the Geometry of Numbers | |||||
401-3058-00L | Kombinatorik I Findet dieses Semester nicht statt. | W | 4 KP | 2G | N. Hungerbühler | |
Kurzbeschreibung | Der Kurs Kombinatorik I und II ist eine Einführung in die abzählende Kombinatorik. | |||||
Lernziel | Die Studierenden sind in der Lage, kombinatorische Probleme einzuordnen und die adaequaten Techniken zu deren Loesung anzuwenden. | |||||
Inhalt | Inhalt 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 / Besonderes | Wer 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. | |||||
Auswahl: Geometrie | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-3056-00L | Endliche Geometrien I | W | 4 KP | 2G | N. Hungerbühler | |
Kurzbeschreibung | Endliche 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. | |||||
Lernziel | Endliche 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. | |||||
Inhalt | Endliche 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. | |||||
401-3556-20L | Topics in Symplectic Topology | W | 6 KP | 3V | P. Biran | |
Kurzbeschreibung | This will be an introductory course in symplectic geometry and topology. We will cover the simplest instances of symplectic rigidity phenomena, and techniques to detect and study them. The last part of the course will be devoted to more advanced techniques such as Floer theory. | |||||
Lernziel | Get acquainted with the basics of symplectic topology and phenomena of symplectic rigidity. | |||||
Literatur | 1) Book: "Introduction to Symplectic Topology", 3'rd edition, by McDuff and Salamon. Oxford Graduate Texts in Mathematics 2) Some published articles that will be announced during the semester. | |||||
401-3574-61L | Introduction to Knot Theory Findet dieses Semester nicht statt. | W | 6 KP | 3G | ||
Kurzbeschreibung | Introduction 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. | |||||
Lernziel | The 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. | |||||
Inhalt | Definition 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.....) | |||||
Literatur | An extensive bibliography will be handed out in the course. | |||||
Voraussetzungen / Besonderes | Prerequisites are some elementary knowledge of algebra and topology. | |||||
Auswahl: Analysis (noch) kein Angebot in diesem Semester | ||||||
Auswahl: Numerische Mathematik (noch) kein Angebot in diesem Semester | ||||||
Auswahl: Wahrscheinlichkeitstheorie, Statistik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
401-6102-00L | Multivariate Statistics Findet dieses Semester nicht statt. | W | 4 KP | 2G | keine Angaben | |
Kurzbeschreibung | Multivariate 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. | |||||
Lernziel | After 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 | |||||
Inhalt | Visualization / Principal component analysis / Multidimensional scaling / The multivariate Normal distribution / Factor analysis / Supervised learning / Cluster analysis | |||||
Skript | None | |||||
Literatur | The course will be based on class notes and books that are available electronically via the ETH library. | |||||
Voraussetzungen / Besonderes | Target 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. | |||||
401-4626-00L | Advanced Statistical Modelling: Mixed Models | W | 4 KP | 2V | M. Mächler | |
Kurzbeschreibung | Mixed Models = (*| generalized| non-) linear Mixed-effects Models, extend traditional regression models by adding "random effect" terms. In applications, such models are called "hierarchical models", "repeated measures" or "split plot designs". Mixed models are widely used and appropriate in an aera of complex data measured from living creatures from biology to human sciences. | |||||
Lernziel | - Becoming aware how mixed models are more realistic and more powerful in many cases than traditional ("fixed-effects only") regression models. - Learning to fit such models to data correctly, critically interpreting results for such model fits, and hence learning to work the creative cycle of responsible statistical data analysis: "fit -> interpret & diagnose -> modify the fit -> interpret & ...." - Becoming aware of computational and methodological limitations of these models, even when using state-of-the art software. | |||||
Inhalt | The lecture will build on various examples, use R and notably the `lme4` package, to illustrate concepts. The relevant R scripts are made available online. Inference (significance of factors, confidence intervals) will focus on the more realistic *un*balanced situation where classical (ANOVA, sum of squares etc) methods are known to be deficient. Hence, Maximum Likelihood (ML) and its variant, "REML", will be used for estimation and inference. | |||||
Skript | We will work with an unfinished book proposal from Prof Douglas Bates, Wisconsin, USA which itself is a mixture of theory and worked R code examples. These lecture notes and all R scripts are made available from Link | |||||
Literatur | (see web page and lecture notes) | |||||
Voraussetzungen / Besonderes | - We assume a good working knowledge about multiple linear regression ("the general linear model') and an intermediate (not beginner's) knowledge about model based statistics (estimation, confidence intervals,..). Typically this means at least two classes of (math based) statistics, say 1. Intro to probability and statistics 2. (Applied) regression including Matrix-Vector notation Y = X b + E - Basic (1 semester) "Matrix calculus" / linear algebra is also assumed. - If familiarity with [R](Link) is not given, it should be acquired during the course (by the student on own initiative). | |||||
401-4627-00L | Empirical Process Theory and Applications | W | 4 KP | 2V | S. van de Geer | |
Kurzbeschreibung | Empirical process theory provides a rich toolbox for studying the properties of empirical risk minimizers, such as least squares and maximum likelihood estimators, support vector machines, etc. | |||||
Lernziel | ||||||
Inhalt | In this series of lectures, we will start with considering exponential inequalities, including concentration inequalities, for the deviation of averages from their mean. We furthermore present some notions from approximation theory, because this enables us to assess the modulus of continuity of empirical processes. We introduce e.g., Vapnik Chervonenkis dimension: a combinatorial concept (from learning theory) of the "size" of a collection of sets or functions. As statistical applications, we study consistency and exponential inequalities for empirical risk minimizers, and asymptotic normality in semi-parametric models. We moreover examine regularization and model selection. | |||||
Auswahl: Finanz- und Versicherungsmathematik | ||||||
Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
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 | C. Czichowsky | |
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 Link | |||||
Literatur | Quantitative Risk Management: Concepts, Techniques and Tools AJ McNeil, R Frey and P Embrechts Princeton University Press, Princeton, 2015 (Revised Edition) Link | |||||
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 Link. Basic knowledge in probability theory is assumed, in particular conditional expectations. |
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