Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-60-14-M-6

Monte Carlo Algorithms (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-60-14-M-6 Monte Carlo Algorithms 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg. SuSe
Level [6] Master (General)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics
Livecycle-State [NORM] Active

Notice

Without a proof of successful participation in the exercise classes, only 6 credit points will be awarded for the module.

The module is offered at least every second summer semester.

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-60-14-K-6
Monte Carlo Algorithms
P 84 h 186 h
U-Schein
- PL1 9.0 irreg. SuSe
  • About [MAT-60-14-K-6]: Title: "Monte Carlo Algorithms"; Presence-Time: 84 h; Self-Study: 186 h
  • About [MAT-60-14-K-6]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 84191 ("Monte Carlo Algorithms")

Evaluation of grades

The grade of the module examination is also the module grade.


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

Upon successful completion of the module, 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.. They understand the proofs presented in the lecture and are able to reproduce and explain them.

By completing the exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the course.

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.

Registration

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

Requirements for attendance of the module (informal)

Modules:

Requirements for attendance of the module (formal)

None

References to Module / Module Number [MAT-60-14-M-6]

Course of Study Section Choice/Obligation
[INF-88.79-SG] M.Sc. Computer Science [Core Modules (non specialised)] Formal Fundamentals [WP] Compulsory Elective
[MAT-88.105-SG] M.Sc. Mathematics [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective
[MAT-88.118-SG] M.Sc. Industrial Mathematics [Core Modules (non specialised)] General Mathematics [WP] Compulsory Elective
[MAT-88.276-SG] M.Sc. Business Mathematics [Core Modules (non specialised)] General Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective
[MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics [Core Modules (non specialised)] Statistics and Computational Methods [WP] Compulsory Elective