Syllabus
Registration via LPIS
| Day | Date | Time | Room |
|---|---|---|---|
| Tuesday | 11/27/18 | 09:00 AM - 11:00 AM | TC.4.03 |
| Wednesday | 11/28/18 | 12:30 PM - 02:30 PM | D3.0.225 |
| Tuesday | 12/04/18 | 09:00 AM - 11:00 AM | TC.4.03 |
| Wednesday | 12/05/18 | 12:30 PM - 02:30 PM | TC.5.03 |
| Tuesday | 12/11/18 | 09:00 AM - 11:00 AM | TC.4.03 |
| Wednesday | 12/12/18 | 12:30 PM - 02:30 PM | TC.4.03 |
| Tuesday | 12/18/18 | 09:00 AM - 11:00 AM | TC.4.03 |
| Wednesday | 12/19/18 | 12:30 PM - 02:30 PM | TC.2.01 |
| Tuesday | 01/08/19 | 09:00 AM - 11:00 AM | TC.4.03 |
| Wednesday | 01/09/19 | 12:30 PM - 02:30 PM | TC.5.03 |
| Tuesday | 01/15/19 | 09:00 AM - 11:00 AM | TC.4.03 |
| Wednesday | 01/16/19 | 12:30 PM - 02:30 PM | TC.5.27 |
| Monday | 01/28/19 | 09:00 AM - 11:00 AM | TC.0.01 ERSTE |
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.
- 30% weekly exams
- 30% midterm exam
- 40% final exam
There will be no opportunity to retake the exams.
- 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.
Download handout for the course at http://statmath.wu.ac.at/courses/qfin_prob/
| Unit | Date | Contents |
|---|---|---|
| 1 | 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 |
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| 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 |
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| 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 |
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| 4 | Multivariate distributions Independence and product measures – Lebesgue measure – densities in R – transformation – Gaussian distribution. Reference: Handout chapter 5 |
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| 5 | Characteristic functions Definition and properties of characteristic functions – uniqueness – sums of independent random variables – Gaussian distributionReference: Handout chapter 6 |
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| 6 | Conditional expectation Definition of conditional expectation – properties – partitions – projections – conditional distributions Reference: Handout chapter 7 |
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| 7 | Final Exam |
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