Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB and Python programmingand knowledge of numerical mathematics at ETH BSc level.

This course is on the numerical approximations of stochastic ordinary differential equations (SDEs) driven by Brownian motions and Lévy processes. SDEs have several applications, for example in financial engineering.The contents cover stochastic processes, stochastic calculus, well-posedness results for SDEs, strong and weak approximations of SDEs, and simulation via Monte Carlo methods.

TO BE ADJUSTEDIntroduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB and Python programmingand knowledge of numerical mathematics at ETH BSc level.

This course will give an introduction to numerical methods, aimed at mathematics and physics majors. It covers numerical linear algebra, quadrature, interpolation and approximation methods as well as their error analysis and implementation.

This course gives an introduction to mathematical analysis of numerical methods, aimed at mathematics majors.Prerequisites are 1-year courses on real analysis and linear algebra.The course covers numerical linear algebra, quadrature, interpolation and approximation, and least squares as well as proof techniques and main results on their mathematical error analysis and implementation.

This course will give an introduction to numerical methods, aimed at mathematics majors. It covers numerical linear algebra, quadrature, interpolation and approximation methods as well as their error analysis and implementation.

The Seminar will address recent mathematical results on neural network based operator learning. Expression rate bounds, curse of complexity, statistical learning of operators.

This seminar will review recent _mathematical results_ on approximation power of deep neural networks (DNNs). The focus will be on mathematical proof techniques to obtain approximation rate estimates (in terms of neural network size and connectivity) on various classes of input data including, in particular, selected types of PDE solutions.

The Seminar will review recent research papers and research results on the mathematical analysis (convergence rates, error vs. work, expression rate bounds, etc.) of deep learning based numerical methods for partial differential equations (PDEs).Particular attention is on high-dimensional PDEs as arise in financial modelling, physics, etc.

This course gives a comprehensive introduction into the numerical treatment of elliptic boundary value problems and parabolic evolution problems. Emphasis is on theory and the foundations of numerical methods.Practical exercises include MATLAB and python implementations of finite difference methods, finite element methods and time integration schemes.

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.

Methods for the numerical solution of partial differential equations of elliptic, parabolic and hyperbolic type. Finite Element, Finite Difference and Finite Volume Methods. A-priori and a-posteriori error estimation. MATLAB implementation in one and two spatial dimensions.

This course is on the numerical approximations of stochastic ordinary differential equations (SDEs) driven by Brownian motions and Lévy processes. SDEs have several applications, for example in financial engineering.The contents cover stochastic processes, stochastic calculus, well-posedness results for SDEs, strong and weak approximations of SDEs, and simulation via Monte Carlo methods.