# Mete Soner: Catalogue data in Autumn Semester 2016

Name | Prof. Dr. Mete Soner |

Field | Financial Mathematics |

Address | Professur für Finanzmathematik ETH Zürich, HG G 54.3 Rämistrasse 101 8092 Zürich SWITZERLAND |

mete.soner@math.ethz.ch | |

URL | https://soner.princeton.edu |

Department | Mathematics |

Relationship | Professor Emeritus |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-0363-10L | Analysis III | 3 credits | 2V + 1U | M. Soner | |

Abstract | Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics. | ||||

Objective | Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partial differential equations. The first lecture is on Thursday, September 29 13-15 in HG F 7 and video transmitted into HG F 5. The exercises Sheet are here: http://www.vvz.ethz.ch/Vorlesungsverzeichnis/lerneinheitPre.do?semkez=2016W&lang=de&ansicht=LERNMATERIALIEN&lerneinheitId=108855 The coordinator is Claudio Sibilia (see https://www.math.ethz.ch/the-department/people.html?u=sibiliac) The first exercise session is on Thursday, September 22 or resp. Friday, September 23. If you would like feedback on your work, please give it to your course assistent or leave it in the box of your course assistant in HG F 27. The due Date is one week later the assignment. Office hour (Praesenz): Thursday 16-17, NO E 39. | ||||

Content | Laplace Transforms: - Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting - Transforms of Derivatives and Integrals, ODEs - Unit Step Function, t-Shifting - Short Impulses, Dirac's Delta Function, Partial Fractions - Convolution, Integral Equations - Differentiation and Integration of Transforms Fourier Series, Integrals and Transforms: - Fourier Series - Functions of Any Period p=2L - Even and Odd Functions, Half-Range Expansions - Forced Oscillations - Approximation by Trigonometric Polynomials - Fourier Integral - Fourier Cosine and Sine Transform Partial Differential Equations: - Basic Concepts - Modeling: Vibrating String, Wave Equation - Solution by separation of variables; use of Fourier series - D'Alembert Solution of Wave Equation, Characteristics - Heat Equation: Solution by Fourier Series - Heat Equation: Solutions by Fourier Integrals and Transforms - Modeling Membrane: Two Dimensional Wave Equation - Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series - Solution of PDEs by Laplace Transform Download the syllabus: https://polybox.ethz.ch/index.php/s/bu5KY8vWNMOnaAa | ||||

Lecture notes | Alessandra Iozzi's Lecture notes: https://polybox.ethz.ch/index.php/s/RcsFm70tWCheSqH Errata: https://polybox.ethz.ch/index.php/s/VKh86gvQRTwIE0w | ||||

Literature | E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 9. Auflage, 2011 C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed. G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003. Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005 For reference/complement of the Analysis I/II courses: Christian Blatter: Ingenieur-Analysis (Download PDF) | ||||

401-3910-66L | Mean Field Games Number of participants limited to 15. | 4 credits | 2S | M. Burzoni, M. Soner | |

Abstract | The analysis of differential games with a large number of players finds applications in various research fields, from physics to economics and finance. The aim of Mean Field Games theory is to provide a suitable approximation of such problems with a higher tractability. | ||||

Objective | This course aims to give a broad understanding of the basic ideas of Mean Field Games, the main mathematical tools and the possible applications. | ||||

Content | We first present and analyze toy models of Mean Field Games in order to familiarize with the subject and to understand what kind of problems can be solved with this theory. We recall some basic principles of optimal control theory and stochastic differential equations. We explore two different approaches to Mean Field Games. From an analytic point of view it consists of a coupled system of PDEs. From a probabilistic point of view it amounts to a particular type of stochastic differential equations. | ||||

Literature | 1) Notes on Mean Field Games. P. Cardaliaguet 2) Mean Field Games. J.M. Lasry, P.L. Lions 3) Probabilistic theory of Mean Field Games and applications. R. Carmona, F. Delarue | ||||

Prerequisites / Notice | Basic courses in analysis including basic knowledge of ordinary/partial differential equations. Basic knowledge of stochastic analysis including Brownian Motion and stochastic differential equations. | ||||

401-5910-00L | Talks in Financial and Insurance Mathematics | 0 credits | 1K | P. Cheridito, M. Schweizer, M. Soner, J. Teichmann, M. V. Wüthrich | |

Abstract | Research colloquium | ||||

Objective | |||||

Content | Regular research talks on various topics in mathematical finance and actuarial mathematics | ||||

406-0353-AAL | Analysis III Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 4 credits | 9R | M. Soner | |

Abstract | Introduction to partial differential equations. Differential equations which are important in applications are classified and solved. Elliptic, parabolic and hyperbolic differential equations are treated. The following mathematical tools are introduced: Laplace transforms, Fourier series, separation of variables, methods of characteristics. | ||||

Objective | Mathematical treatment of problems in science and engineering. To understand the properties of the different types of partlial differentail equations. | ||||

Content | Laplace Transforms: - Laplace Transform, Inverse Laplace Transform, Linearity, s-Shifting - Transforms of Derivatives and Integrals, ODEs - Unit Step Function, t-Shifting - Short Impulses, Dirac's Delta Function, Partial Fractions - Convolution, Integral Equations - Differentiation and Integration of Transforms Fourier Series, Integrals and Transforms: - Fourier Series - Functions of Any Period p=2L - Even and Odd Functions, Half-Range Expansions - Forced Oscillations - Approximation by Trigonometric Polynomials - Fourier Integral - Fourier Cosine and Sine Transform Partial Differential Equations: - Basic Concepts - Modeling: Vibrating String, Wave Equation - Solution by separation of variables; use of Fourier series - D'Alembert Solution of Wave Equation, Characteristics - Heat Equation: Solution by Fourier Series - Heat Equation: Solutions by Fourier Integrals and Transforms - Modeling Membrane: Two Dimensional Wave Equation - Laplacian in Polar Coordinates: Circular Membrane, Fourier-Bessel Series - Solution of PDEs by Laplace Transform | ||||

Literature | E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10. Auflage, 2011 C. R. Wylie & L. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 6th ed. G. Felder, Partielle Differenzialgleichungen für Ingenieurinnen und Ingenieure, hypertextuelle Notizen zur Vorlesung Analysis III im WS 2002/2003. Y. Pinchover, J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005 For reference/complement of the Analysis I/II courses: Christian Blatter: Ingenieur-Analysis (Download PDF) | ||||

Prerequisites / Notice | Up-to-date information about this course can be found at: http://www.math.ethz.ch/education/bachelor/lectures/hs2013/other/analysis3_itet | ||||

406-2604-AAL | Probability and StatisticsEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 7 credits | 15R | M. Soner | |

Abstract | Introduction to probability and statistics with many examples, based on chapters from the books "Probability and Random Processes" by G. Grimmett and D. Stirzaker and "Mathematical Statistics and Data Analysis" by J. Rice. | ||||

Objective | The goal of this course is to provide an introduction to the basic ideas and concepts from probability theory and mathematical statistics. In addition to a mathematically rigorous treatment, also an intuitive understanding and familiarity with the ideas behind the definitions are emphasized. Measure theory is not used systematically, but it should become clear why and where measure theory is needed. | ||||

Content | Probability: Chapters 1-5 (Probabilities and events, Discrete and continuous random variables, Generating functions) and Sections 7.1-7.5 (Convergence of random variables) from the book "Probability and Random Processes". Most of this material is also covered in Chap. 1-5 of "Mathematical Statistics and Data Analysis", on a slightly easier level. Statistics: Sections 8.1 - 8.5 (Estimation of parameters), 9.1 - 9.4 (Testing Hypotheses), 11.1 - 11.3 (Comparing two samples) from "Mathematical Statistics and Data Analysis". | ||||

Literature | Geoffrey Grimmett and David Stirzaker, Probability and Random Processes. 3rd Edition. Oxford University Press, 2001. John A. Rice, Mathematical Statistics and Data Analysis, 3rd edition. Duxbury Press, 2006. |