Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-60-14-K-6

Monte Carlo Algorithms (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
4 V Lecture 6.0 CP 56 h 124 h
2 U Exercise class (in small groups) 3.0 CP 28 h 62 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg. SuSe
Level [6] Master (General)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Livecycle-State [NORM] Active

Notice

The course is offered at least every second summer semester.

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (ungraded)
  • Examination number (Study achievement): 84037 ("Exercise Class Monte Carlo Algorithms")
  • Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

Contents

Monte Carlo algorithms are the algorithms which use randomness. The course gives an introduction to this important basic algorithmic technique in mathematics and computer science.

It discusses the topics

  • Direct Simulation
  • Simulation of distributions
  • Variance reduction
  • Markov Chain Monte Carlo algorithms
  • High-dimensional integration

and applications in physics as well as in financial and actuarial mathematics

Competencies / intended learning achievements

The students have developed a basic understanding of the construction, analysis and applications of Monte Carlo algorithms. They have gained practical experience of using such algorithms and insights into different application fields and they are able to critically assess the applicability and limitations of the algorithms.

Literature

  • T. Müller-Gronbach, E. Novak, K. Ritter: Monte Carlo-Algorithmen,
  • S. Asmussen, P.W. Glynn: Stochastic Simulation,
  • E. Behrends: Introduction to Markov Chains,
  • P. Brémaud: Markov Chains,
  • P. Glasserman: Monte Carlo Methods in Financial Engineering,
  • C. Lemieux: Monte Carlo and Quasi-Monte Carlo Sampling,
  • R. Motwani, P. Raghavan: Randomized Algorithms,
  • J.F. Traub, G.W. Wasilkowski, H. Wozniakowski: Information-based Complexity.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-60-14-K-6]

Module Name Context
[MAT-60-14-M-6] Monte Carlo Algorithms P: Obligatory 4V+2U, 9.0 LP
Course-Pool Name
[MAT-50-4V-KPOOL-4] Elective Courses Optimisation and Stochastics (4V, B.Sc.)
[MAT-70-4V-KPOOL-4] Elective Courses Analysis and Stochastics (4V, B.Sc.)
[MAT-70-KPOOL-4] Specialisation Analysis and Stochastics (B.Sc.)
[MAT-80-4V-KPOOL-4] Elective Courses Modelling and Scientific Computing (4V, B.Sc.)