14266 - Stochastic Analysis Modulübersicht

Module Number: 14266
Module Title:Stochastic Analysis
  Stochastische Analysis
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. Hartmann, Carsten
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 8
Learning Outcome:After successfully completing the module, students are familiar with the most important concepts and relationships of stochastic analysis. They can apply probability theory and analytical methods to the time development of random variables. Students are able to investigate economic, engineering or scientific models using stochastic analysis. In addition, they have gained experience in independent scientific work based on specific questions.
Contents:
  • basic notions of stochastic processes
  • conditional expectation, martingales, stochastic integrals
  • Ito and Malliavin calculi
  • stochastic differential equations and their application in science, engineering and finance (e.g. Black and Scholes model, option pricing, Gibbs measures)
Recommended Prerequisites:Knowledge of the content of the modules
  • 11217 : Wahrscheinlichkeitstheorie
  • 13889 : Stochastic Processes
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Self organised studies / 180 Hours
Teaching Materials and Literature:
  • R. Korn, E. Korn. Optionsbewertung und Portfolio-Optimierung, Vieweg, 2001.
  • I. Karatzas, S.E. Shreve. Brownian Motion and Stochastic Calculus. Springer, 1991.
  • T. Mikosch. Elementary Stochastic Calculus with Finance in View. World Scientific, 2000.
  • I. Shigekawa. Stochastic Analysis. AMS, 2004.
  • S.R.S. Varadhan. Stochastic Processes. AMS, 2007.
Module Examination:Final Module Examination (MAP)
Assessment Mode for Module Examination:
  • Written examination, 90 min. OR
  • Oral examination, 30 min.
It will be announced in the first lecture whether the examination will organized in written or oral form.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • no assignment
Remarks:
  • Study programme Mathematics M.Sc.: Compulsory elective module in the complex „Stochastics“
  • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
  • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Vertiefung“, in limited extend
Module Components:
  • Lecture: Stochastic Analysis
  • Related examination
Components to be offered in the Current Semester:
  • no assignment