Methods of Monte Carlo Simulation
Dr. Tim Brereton
Time and Place
Friday, 8-10 am (N24-131)
Monday, 1-2 pm (N24-131)
2 hours lecture and 1 hour excercise
|Credit points:||4 for Bachelor students||(lecture only)|
|6 for Master students||(lecture and reading course)|
Basic knowledge of probability calculus and statistics as taught, for example, in "Elementare Wahrscheinlichkeitsrechnung und Statistik".
Bachelor students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie"; Master students in "Finance"
Master's students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie" can also take the course. In order to gain credit, they will be required to do some additional reading (1 - 2 hours per week) and take a different exam, which will be based on the reading material as well as the lectures.
This course gives a broad overview of Monte Carlo methods. These methods include many important tools for students interested in applied probability, finance and statistics. The course will cover the following topics:
- Pseudo-random numbers and quasi-random numbers
- Generating random variables
- Generating stochastic processes
- Markov Chain Monte Carlo
- Variance reduction
- Gradient estimation
- Stochastic optimization
Examples will be given of applications in finance, probability, statistics and the physical sciences.
Master's students taking the reading course will be required to be familiar with Dirk Kroese's lecture notes (with the exception of sections 4.6 - 4.9) . These notes contain several chapters and sections that will not be covered in class. The exam will cover this material. In order to understand this material, students should complete the exercises given in the notes.
The material you need to cover (with study suggestions) is given here:
Here are some example exam questions for the Master's course (they are a bit harder than the ones you will see on the exam):
Example exam questions
Requirements and Exam
In order to participate in the final exam, it is necessary to earn 50% of the points on all problem sheets. Students who want to do so are kindly asked to register for the 'Vorleistung' in the LSF-'Hochschulportal'.
Time and place
Thursday, February 27 (10 am - noon) in H14
Friday, April 11 (10 am - noon) in H14
Participants will be allowed to bring one handwritten A4 sheet (both sides) containing useful results from the lecture and exercise classes. Copies and printouts will not be allowed.
Here is a practice exam. NOTE!!! These are not the same questions as those on the actual exam!!!
The second exam is corrected!
You can find the number of points you obtained in the SLC as an extra exercise sheet (marked as "Prüfungsleistung"). The associated marks are indicated in the following tabular (it's the same for first and second exam and for both exam types):
|1,0||38 - 44|
|1,3||35,5 - 37,5|
|1,7||33 - 35|
|2,0||30,5 - 32,5|
|2,3||28 - 30|
|2,7||26 - 27,5|
|3,0||23,5 - 25,5|
|3,3||21 - 23|
|3,7||18,5 - 20,5|
|4,0||16 - 18|
|5,0||0 - 15,5|
The post-exam review will take place on Wednesday, April 16 from 9 to 10 am in Lisa Handl's office (room 1.42 in Helmholtzstr. 18).
Problem Sheet 01 Matlab Solution 01
Problem Sheet 02 Matlab Solution 02
Problem Sheet 03 Matlab Solution 03
Problem Sheet 04 Matlab Solution 04
Problem Sheet 05 Matlab Solution 05
Problem Sheet 06 Matlab Solution 06
Problem Sheet 07 Matlab Solution 07
Problem Sheet 08 Matlab Solution 08 Ex. 2 Plot
Problem Sheet 09 Matlab Solution 09
Problem Sheet 10 Matlab Solution 10
Problem Sheet 11 Matlab Solution 11
Problem Sheet 12 Matlab Solution 12
In order to receive points for your problem sheets, a registration at SLC is required.
The first part of the lecture notes is now online. They will be updated frequently over the next week or so. Please email me if you find any mistakes.
The lecture are loosely based on the lecture notes of Prof. Dr. Dirk P. Kroese from the University of Queensland, Brisbane, Australia.
Information on discrete-time Markov chains can be found here:
Asmussen, S. and P. Glynn. Stochastic Simulation. Springer, 2007.
Fishman, G. Monte Carlo: Algorithms and Applications. Springer, 2003.
Gamerman, D. and H. Lopes. Stochastic Simulation for Bayesian Inference, Second Edition. Chapman & Hall, 2006.
Glasserman, P. Monte Carlo Methods in Financial Engineering. Springer, 2004.
Kroese, D. P., T. Taimre and Z. Botev. Handbook of Monte Carlo Methods. Wiley, 2011.
Robert, C. P. and G. Casella. Monte Carlo Statistical Methods, Second Edition. Springer, 2005.
Ross, S. M. Simulation, Fifth Edition. Academic Press, 2012.
Rubinstein, R. and D. P. Kroese. Simulation and the Monte Carlo Method. Wiley, 2007.
If you missed the post-exam review and still want to have a look at your exam, you can do so on Wednesday, April 23 from 11 to 11:30 am in Lisa Handl's office. Please understand that we won't offer any extra appointments besides that one.
The second exam is corrected! You can see the points you obtained in your SLC account, a tabular with the corresponding marks is on this page (section "Requirements and Exam").
We now have printed copies of the lecture notes: You can get them (for free) in Dr. Brereton's office (room 1.43, Helmholtzstr. 18).
The lecture notes have been updated again.
A practice exam is now online and so are some study suggestions for the reading course.
The second exam has been shifted to Friday, April 11 (10 am - noon) in H14. It will NOT take place on Good Friday (Karfreitag)!
The exam dates are fixed:
The first exam will take place on Thursday, February 27 (10 am - noon) in H14, the second exam on Friday, April 11 (10 am - noon) in H14.