The course provides an introduction into the mathematics of probability and stochastics, which is necessary to understand and apply it in finance, statistics and mathematical finance.

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.

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

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 midterm exam. There will be a final retake exam and information about its schedule will be given out at the end of the semester. The final retake will likely be near end of February.

• 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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email: paul.eisenberg@wu.ac.at