Methods of Monte Carlo Simulation II
Lecturer
Dr. Tim Brereton
Teaching assistant
Matthias Neumann
Time and Place
Lecture
Friday, 10-12 am (220, Helmholtzstr. 18)
Excercise session
Thursday, 1 - 2 pm (220, Helmholtzstr. 18)
Type
2 hours lecture and 1 hour excercise
| Credit points: | 4 | lecture only |
| 6 | lecture and reading course |
Prerequisites
Basic knowledge of probability calculus and statistics as taught, for example, in "Elementare Wahrscheinlichkeitsrechnung und Statistik". In particular, the course Methods of Monte Carlo Simulation (winter term 2013/14) is not required.
Intended Audience
Bachelor students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie"; Master students in "Finance"
Students from other fields (in particular Physics, Computer Science or Chemistry) are welcome as well; the respective examination board (Prüfungsausschuss) decides on the possible recognition of examinations.
Contents
This course is not a sequel to Methods of Monte Carlo Simulation I (MMCS1), but rather a complimentary course. As such, MMCS1 is not a required prerequisite.
In MMCS1, we considered generic Monte Carlo methods for efficiently solving estimation and optimization problems. In this course (MMCS2), we instead focus on simulating probabilistic objects, including many important stochastic processes and structures.
No prior knowledge of these probabilistic objects will be assumed. They will be introduced and some key properties will be examined. We will focus on efficiently generating replicates of these on a computer and using these replicates to solve a number of interesting problems.
Some of the objects we will consider are: stochastic processes that model the movement of particles and the evolution of stock prices; point processes that can model the distribution of a particular type of tree in a forest or the number of defaults in a portfolio of bonds; and spatial random objects that can model magnetization or the distribution of yearly rainfall in various regions of Germany.
This course would be ideal for students interested in learning about applied stochastic modeling.
Reading Course
Students may choose if they want to take a reading course (in addition to the lectures) in order to gain 6 credit points instead of 4.
For the reading course, students will have to study some additional material (which will not be covered in class). The material to read will be announced in the lectures / exercises and will be provided online each week. Moreover, the participants of the reading course will have to write an extended exam, which will cover this additional material.
The first reading is here:
The answer to the question in the exercises will be discussed at 12:30 on Thursday (immediately before the exercises).
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
First exam: August 9, 9.30 am (N24, H12)
Second exam: October 7, 2.00 pm (N24, H15)
For the exams you will NOT be allowed to bring any notes. Moreover, calculators are not permitted (you won't need one).
The 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:
| 1,0 | 48 - 46 | ||
| 1,3 | 45.5 - 44 | ||
| 1,7 | 43.5 - 41.5 | ||
| 2,0 | 41 - 39 | ||
| 2,3 | 38.5 - 36.5 | ||
| 2,7 | 36 - 34 | ||
| 3,0 | 33.5 - 31.5 | ||
| 3,3 | 31 - 29 | ||
| 3,7 | 29 - 26.5 | ||
| 4,0 | 26 - 24 | ||
| 5,0 | 0 - 23.5 | ||
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:
| 1,0 | 52 - 49 | ||
| 1,3 | 48.5 - 46.5 | ||
| 1,7 | 46 - 44 | ||
| 2,0 | 43.5 - 41.5 | ||
| 2,3 | 41 - 39 | ||
| 2,7 | 38.5 - 36.5 | ||
| 3,0 | 36 - 34 | ||
| 3,3 | 33.5 - 31.5 | ||
| 3,7 | 31 - 29 | ||
| 4,0 | 28.5 - 26 | ||
| 5,0 | 25.5 - 0 | ||
Problem Sheets
In order to receive points for your problem sheets, a registration at SLC is required.
Exercise about reading material 2
Lecture Notes
Lecture notes will be provided roughly one week after the correpsonding lectures.
The lecture notes are here:
Literature
Asmussen, S. and P. Glynn. Stochastic Simulation. Springer, 2007.
Brémaud, P. Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer, 1999.
Cont, R. and P. Tankov. Financial Modeling with Jump Processes. Chapman & Hall/CRC, 2003.
Glasserman, P. Monte Carlo Methods in Financial Engineering. Springer, 2004.
Graham, C. and D. Talay. Stochastic Simulation and Monte Carlo Methods: Mathematical Foundations of Stochastic Simulation. Springer, 2013.
Kroese, D. P., T. Taimre and Z. Botev. Handbook of Monte Carlo Methods. Wiley, 2011.
Møller, J. and Waagepetersen, R. P. Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, 2003.
Ross, S. M. Simulation, Fifth Edition. Academic Press, 2012.
Winkler, G. Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction. Springer, 2003.
Contact
Lecturer
- timothy.brereton(at)uni-ulm.de
- Office hours on appointment
- Phone: +49 (0)731/50-23590
- Homepage
Teaching assistant
- matthias.neumann(at)uni-ulm.de
- Office hours on appointment
- Phone: +49 (0)731/50-23617
- Homepage
News
The post-exam review will take place on Thursday, August 14 from 2 to 3 pm in Dr. Brereton's office (room 1.43 in Helmholtzstr. 18)
The exam will take place in N24, H12.
Lecture notes updated
The exam section has been updated. In particular, you will not be allowed to bring any notes or calculators.
Please register for the prerequisites at the LSF-portal. Prerequisites for the exam without reading course have the number 13269, while prerequisites for the exam including the reading course have number 13325.
Lecture notes have been updated.