401-4657-00L  Numerical Analysis of Stochastic Ordinary Differential Equations

Semester Autumn Semester 2013
Lecturers A. Jentzen
Periodicity yearly course
Language of instruction English
Comment Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"


Abstract Course on numerical approximation 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.
Objective The 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.
Content Generation 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 notes Printed Lecture Notes will be distributed in class.
Literature P. 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 / Notice Prerequisites:

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

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

b) recommended courses:
Stochastic Processes.