Lecturer
Dr. Tim Brereton

Teaching assistant
Lisa Handl

Time and Place

Lecture
Friday, 8-10 am (220, Helmholtzstr. 18)

Excercise session
Thursday, 4-6 pm (E20, Helmholtzstr. 18) every second week

We agreed to start at 8:30 on Fridays instead of a break.

Type

 2 hours lecture and 1 hour excercise

Prerequisites

Basic knowledge of probability calculus and statistics as taught, for example, in "Elementare Wahrscheinlichkeitsrechnung und Statistik".

Intended Audience

The regular version of the course is accessible to Bachelor students in "Mathematik", "Wirtschaftsmathematik" and "Mathematische Biometrie" and Master students in "Finance".

Master 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.

Students in "Master of Finance" can choose if they want to do the lecture only (for 4 credits) or the lecture plus reading course (6 credits).

Contents

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

• Mathematical analysis of Monte Carlo algorithms

• Variance reduction

Examples will be given of applications in finance, probability, statistics and the physical sciences.

Reading Course

The reading course focuses on some stochastic processes (the Poisson process and Gaussian processes). Please let me know if you need any additional background material (I can either add it to the notes or direct you towards some books).

The notes for the reading course are here: reading course.

Here are the practice exercises: practice questions

Requirements and Exam

In order to participate in the final exam, it is necessary to earn 50% of the points on all theory questions and 50% of the points on all programming questions on the problem sheets. Students who want to do so are kindly asked to register for the 'Vorleistung' in the LSF-'Hochschulportal'. Please make sure you do so for the right version of the course. The module names in the university portal are:

• "MMCS I - Bachelor der mathematischen Studiengänge und Master Finance":
  4 credits, no reading course, accessible to Bachelor students in Ma/WiMa/MaBi and students in Master of Finance
• "MMCS I - Master":
  6 credits, including reading course, accessible to Master students in Ma/WiMa/MaBi
• "MMCS I - Lecture and Reading Course":
  6 credits, including reading course, accessible to Bachelor students in Ma/WiMa/MaBi and students in Master of Finance

Time and place

First exam:

Monday, February 29
from 10 am to noon in H11

Second exam:

Monday, April 11
from 2 - 4 pm in room 1.42 (Helmholtzstr. 22)

You will be allowed to bring a one-sided (!) handwritten A4 sheet containing useful results from the lecture and exercise classes. Copies and printouts will not be allowed.

The second exams are marked!

You can find the number of points you obtained in the SLC in the section "Prüfungsleistung". The associated marks are indicated in the following table (it is the same for first and second exam, with and without reading course):

The post-exam review will take place on Monday, April 18 from 10 to 11 am in Lisa Handl's office (room 1.42 in Helmholtzstr. 18).

Problem Sheets

In order to receive points for your problem sheets, a registration at SLC is required.

Problem Sheet 01     Matlab Solution 01

Problem Sheet 02     Matlab Solution 02

Problem Sheet 03     Matlab Solution 03     box_muller.m

Problem Sheet 04     Matlab Solution 04

Problem Sheet 05     Matlab Solution 05     myrand.m     mybetarnd.m

Problem Sheet 06     Matlab Solution 06

Problem Sheet 07     Matlab Solution 07     second_moment.m

Programming exercises have to be solved in Matlab. Student licenses can be bought for 20 € at O26/5101, or you can use it for free on many computers on campus, see this page for more information.

A short introduction to Matlab can be found here.

Lecture Notes

The lecture notes will be provided here as we go. Please email me if you find any mistakes.

Lecture notes.

Literature

Asmussen, S. and P. Glynn. Stochastic Simulation. Springer, 2007.

Fishman, G. Monte Carlo: Algorithms and Applications. Springer, 2003.

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.

Ross, S. M. Simulation, Fifth Edition. Academic Press, 2012.

Rubinstein, R. and D. P. Kroese. Simulation and the Monte Carlo Method. Wiley, 2007.

Link to the course reserve collection:

https://ulm.ibs-bw.de/aDISWeb/app?service=direct/0/Home/$DirectLink&sp=S127.0.0.1:23002&sp=SWI00001357