Lecturer: | Imma Curato |
Class and Tutorial Teacher:
| Dirk Brandes |
Type:
| MSc. Finance elective course |
News: | There is a block course in the week before the regular start of the lecture period, so from 8th of Oct. until 12th of Oct. The schedule is as follow: - Mon., 08.10.2018: Lecture: 8:45-10:15 He18, 2.20. Lecture: 10:30-12:00 He18, 2.20.
- Tue., 09.10.2018: Tutorial: 8:45-10:15 He18, 2.20. Lecture: 10:30-12:00 He18, 2.20.
- Wed., 10.10.2018: Lecture: 8:45-10:15 He18, 2.20. Exercise Class: 10:30-12:00 He18, 2.20.
- Thu., 11.10.2018: Lecture: 8:45-10:15 He18, 2.20. Lecture: 10:30-12:00 He18, 2.20.
- Fri., 12.10.2018: Exercise Class: 8:45-10:15 He18, 1.20.
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| Time and Venue: | Schedule of the course from 15th October until Christmas:
- Lecture: Monday, 10:00-12:00, He18 - 2.20
- First Lecture: 15/10/2018
- Additional Lecture: 8:30-10:00 19/11/2018
- Exercise class: Friday, 08:00-09:00, He18 - E20
- First Exercise class: 19/10/2018
- Tutorial course: Friday, 09:00-10:00, He18 - E20
- First Tutorial course: 19/10/2018
- Additional Exercise Classes/Tutorial Courses: Monday, 08:30-10:00, He18 - 2.20. (12/11/2018 and 10/12/2018)
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Final Exam: | written and closed exam of 90 minutes on Monday, 21st January 2019, 10:00-12:00, He18 - 2.20. Retake of the exam on Thursday, 7th March 2019, 10:00-12:00, He18 - 1.20. To participate in the written exam, you have to register at until Wednesday, 16th of January 2019. |
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 .- 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: | |
| Lecture notes: | | |
| Additional Material: | Refresher in Probability 1 Refresher in Probability 2 | |
