Arnulf Jentzen: Catalogue data in Autumn Semester 2016

Name Dr. Arnulf Jentzen
FieldApplied Mathematics
Address
Seminar für Angewandte Mathematik
ETH Zürich, HG G 58.1
Rämistrasse 101
8092 Zürich
SWITZERLAND
E-mailarnulf.jentzen@math.ethz.ch
URLhttp://www.sam.math.ethz.ch/~jentzena
DepartmentMathematics
RelationshipAssistant Professor

NumberTitleECTSHoursLecturers
401-4475-66LPartial Differential Equations and Semigroups of Bounded Linear Operators Information 4 credits2GA. Jentzen
AbstractIn this course we study the concept of a semigroup of bounded linear operators and we use this concept to investigate existence, uniqueness, and regularity properties of solutions of partial differential equations (PDEs) of the evolutionary type.
ObjectiveThe aim of this course is to teach the students a decent knowledge (i) on semigroups of bounded linear operators, (ii) on solutions of partial differential equations (PDEs) of the evolutionary type, and (iii) on the analytic concepts used to formulate and study such semigroups and such PDEs.
ContentThe course includes content (i) on semigroups of bounded linear operators, (ii) on solutions of partial differential equations (PDEs) of the evolutionary type, and (iii) on the analytic concepts used to formulate and study such semigroups and such PDEs. Key example PDEs that are treated in this course are heat and wave equations.
Lecture notesLecture Notes are available in the lecture homepage (please follow the link in the Learning materials section).
Literature1. Amnon Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York (1983).

2. Klaus-Jochen Engel and Rainer Nagel, One-parameter semigroups for linear evolution equations. Springer-Verlag, New York (2000).
Prerequisites / NoticeMandatory prerequisites: Functional analysis

Start of lectures: Friday, September 23, 2016
For more details, please follow the link in the Learning materials section.
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Information
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
6 credits3V + 1UA. Jentzen
AbstractCourse on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
ObjectiveThe aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
ContentGeneration of random numbers
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Multilevel Monte Carlo methods for SODEs
Applications to computational finance: Option valuation
Lecture notesLecture Notes are available in the lecture homepage (please follow the link in the Learning materials section).
LiteratureP. Glassermann:
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.

P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
Prerequisites / NoticePrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday, September 21, 2016
For more details, please follow the link in the Learning materials section.
401-5650-00LZurich Colloquium in Applied and Computational Mathematics Information 0 credits2KR. Abgrall, H. Ammari, R. Hiptmair, A. Jentzen, S. Mishra, S. Sauter, C. Schwab
AbstractResearch colloquium
Objective