0361 Probability
Assist.Prof. Priv.Doz.Dr. Paul Eisenberg
Contact details
Weekly hours
Language of instruction
11/07/22 to 11/13/22
Registration via LPIS
Notes to the course
Subject(s) Master Programs
Day Date Time Room
Tuesday 11/22/22 10:00 AM - 12:00 PM TC.1.02
Wednesday 11/23/22 12:00 PM - 02:00 PM TC.1.01 OeNB
Tuesday 11/29/22 10:00 AM - 12:00 PM TC.1.01 OeNB
Wednesday 11/30/22 12:00 PM - 02:00 PM D3.0.225
Friday 12/02/22 08:00 AM - 10:00 AM TC.2.02
Tuesday 12/06/22 10:00 AM - 12:00 PM TC.0.01
Wednesday 12/07/22 01:30 PM - 03:30 PM TC.0.01
Friday 12/09/22 12:00 PM - 02:00 PM TC.2.01
Tuesday 12/13/22 09:00 AM - 11:00 AM TC.2.02
Wednesday 12/14/22 12:00 PM - 02:00 PM D3.0.233
Friday 12/16/22 12:00 PM - 02:00 PM TC.2.01
Tuesday 12/20/22 10:00 AM - 12:00 PM TC.2.02
Wednesday 12/21/22 12:30 PM - 02:30 PM TC.0.02
Friday 12/23/22 10:00 AM - 12:00 PM Online-Einheit
Tuesday 01/10/23 10:00 AM - 12:00 PM TC.2.01
Wednesday 01/11/23 12:00 PM - 02:00 PM TC.1.01 OeNB
Friday 01/13/23 12:00 PM - 02:00 PM TC.1.01 OeNB
Tuesday 01/17/23 10:00 AM - 12:00 PM TC.0.02
The course provides an introduction into the mathematics of probability and stochastics, which is necessary to understand and apply the basic concepts of finanial mathematics.
Learning outcomes

After completing this course the student will have the ability to:

  • describe and explain the basic concepts and definitions of measure, expectation, random variable and its distribution, conditional expectation and absolute continuity.
  • work with and apply the basic concepts and definitions of measure, expectation, random variable and its distribution, conditional expectation and absolute continuity.
  • confidently organize and integrate mathematical ideas and information.
  • shift mathematical material quickly and efficiently, and to structure it into a coherent mathematical argument.
  • solve applied problems where skills are required from probability.
Attendance requirements

For this lecture participation is obligatory. Students are allowed to miss a maximum of 20% (no matter if excused or not excused).

Teaching/learning method(s)

The lectures are aimed at providing the theoretical framework, while weekly homework exercises check the study progress. Constant learning is necessary.

  • 30%  weekly homework exercises
  • 30%  midterm exam
  • 40%  final exam

There will be no opportunity to retake the exams.



Prerequisites for participation and waiting lists
  • Successful completion of the units ‘Mathematics I’ and ‘Principles of Finance’;
  • Introductory probability on an undergraduate level (concepts of probability, conditional probability, independence, random variables, discrete distributions, densities, expectation, normal distribution, uniform distribution, binomial and Poisson distribution).

The course is based on the book Probability Essentials (2nd ed., Springer 2004) by J. Jacod. and P. Protter.


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Availability of lecturer(s)

Course ReadingsThe contents of the course are covered by the following reference: JP: J. Jacod and P. Protter (2000). Probability Essentials. Springer. ISBN 3-540-66419-X.Lecture Notes and homework assignments
Unit details
Unit Date Contents

Axioms of probability, independence and conditional probabilityDefinition of algebra and probability – properties of probabilities – conditional probability – independence – Bayes’ Theorem and Partition Equation. Reference: Handout chapter 1,2


Univariate distributions Probabilities on countable spaces – Poisson distribution – Geometric distribution – definition of random variable – expectation – Chebyshev’s inequality – probability measures on the real line – distribution function density – properties of random variables. Reference: Handout chapter 2, 3


Integration Simple random variables – monotone convergence – Fatou’s lemma – dominated convergence – definition and properties of expectation – Cauchy-Schwarz inequality – expectation rule. Reference: Handout chapter 4


Multivariate distributions Independence and product measures – Lebesgue measure – densities in R – transformation – Gaussian distribution. Reference: Handout chapter 5


Conditional expectation Definition of conditional expectation – properties – partitions – projections – conditional distributions Reference: Handout chapter 6


The Radon Nikodym Theorem and complements: Handout chapter 7 -- Apendices

7 Final Exam
Last edited: 2022-11-17