Lecturer: | Alexander Lindner |
Class Teacher: | David Berger |
| Type: | MSc. Finance elective course |
News: | There is a block course in the week before the regular start of the lecture period, so from 7th of Oct. until 11th of Oct. The schedule is as follow: - Mon., 07.10.2019: Lecture: 8:15-11:45 He18, 1.20. Exercise Class: 16:15-17:45 He18, 1.20.
- Tue., 08.10.2019: Lecture: 8:15-11:45 He18, 1.20.
- Wed., 09.10.2019: Lecture: 8:15-11:45 He18, 1.20.
- Fri., 11.10.2019: Lecture: 8:15-11:45 He18, 1.20. Exercise Class: 16:15-17:45 He18, 1.20.
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| Time and Venue: | Schedule of the course from 14th of October until 6th of January: - Lecture: Monday, 08:15-09:45, He18 - 1.20
- First Lecture: 14/10/2019
- Exercise class: Wednesday, 08:15-09:45, He22 - E.04
- First Exercise class: 16/10/2019
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Final Exam: | written and closed exam of 90 minutes on Monday, 27th of January 2020, 08:15-09:45, He18 - 1.20. Retake of the exam on Thursday, 5th of March 2020, 10:00-11:30. To participate in the written exam, you have to register at campusonline.uni-ulm.de until Wednesday, 22th of January 2020. |
Prerequisites: | Analysis I+II and Linear Algebra I. |
Contents: | This course covers the basic but nevertheless relevant (especially for Financial Mathematics I) topics of probability theory in a measure-theoretic approach. Specific topics are - Definition and properties of measure and the Lebesgue integral.
- The fundamentals of probability: probability space, random variables, conditional expectation, modes of convergence, convolutions and characteristic functions, central limit theorem.
- An introduction to statistics: simple random sampling, introduction to estimation techniques.
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Literature: | Available in the library. - H. Bauer, Measure and Integration Theory, De Gruyter Studies in Mathematics, 2011.
- H. Bauer, Probability Theory, De Gruyter Studies in Mathematics, 2011.
- P. Billingsley, Probability and Measure, Wiley, 2012.
- W. Rudin, Real and Complex Analysis, McGraw-Hill International Editions, 1987.
- J. Jacod & P. Protter, Probability Essentials, 2nd edition, Springer, 2004.
- E. Kopp, J. Malczak & T. Zastawniak, Probability for Finance, Cambridge University Press, 2014.
- R. Leadbetter, S. Cambanis, V. Pipiras, A Basic Course in Measure and Probability, Cambridge University Press, 2014.
- A. N. Shiryaev, Probability, 2nd edition, Springer, 1995.
- D. Williams, Probability with Martingales, Cambridge University Press, 1991.
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Exercise sheets: | moodle |
| Lecture notes: | moodle | |
| Additional Material: | Refresher in Probability 1 Refresher in Probability 2 | |
