# An Introduction to Measure Theoretic Probability

 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. Time and Venue: Schedule of the course from 15th October until Christmas:Lecture: Monday, 10:00-12:00, He18 - 2.20First Lecture: 15/10/2018Additional Lecture: 8:30-10:00 19/11/2018Exercise class: Friday, 08:00-09:00, He18 - E20First Exercise class: 19/10/2018Tutorial course: Friday, 09:00-10:00, He18 - E20First Tutorial course: 19/10/2018Additional Exercise Classes/Tutorial Courses: Monday, 08:30-10:00, He18 - 2.20. (12/11/2018 and 10/12/2018) 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 campusonline.uni-ulm.de 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 areDefinition 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. 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. Exercise sheets: Moodle Lecture notes: Moodle Additional Material: Refresher in Probability 1Refresher in Probability 2