Lecture Winter Term 2018/2019

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, 2.20Lecture: 10:30-12:00 He18, 2.20.
  • Wed., 10.10.2018:  Lecture: 8:45-10:15 He18, 2.20Exercise Class: 10:30-12:00 He18, 2.20.
  • Thu.,  11.10.2018:  Lecture: 8:45-10:15 He18, 2.20Lecture: 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 - 2.20
  • First Lecture: 15/10/2018
  • Additional Lecture: 8:30-10:00 19/11/2018
  • Exercise classFriday, 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)

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 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.

 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 1

Refresher in Probability 2