14269 - Financial Mathematics in Continuous Time Modulübersicht

Module Number: 14269
Module Title:Financial Mathematics in Continuous Time
  Finanzmathematik in stetiger Zeit
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Wunderlich, Ralf
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 8
Learning Outcome:After successfully completing the module, students understand the most important concepts of stochastic analysis for modeling stochastic financial markets. They are able to apply solution methods for selected problems in stochastic financial mathematics. Students have gained experience in independent scientific work using the example of topics in financial mathematics.
Contents:
  • Basic concepts of stochastic analysis and the mathematical modeling of financial markets
  • Methods of stochastic optimal control for portfolio optimization
  • Dynamic programming and martingale method
  • Term structure models
Recommended Prerequisites:Knowledge of the contents of modules
  • 11217: Wahrscheinlichkeitstheorie
  • 13889: Stochastic Processes
  • 11350: Finanzmathematik II
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 150 Hours
Teaching Materials and Literature:
  • Björk: Arbitrage Theory in Continuous Time, Oxford, 2009
  • Oksendal: Stochastic Differential Equations, Springer, 2007
  • Korn & Korn: Optionsbewertung und Portfolio-Optimierung. Vieweg+Teubner 2009
  • Fleming & Soner: Controlled Markov Processes and Viscosity Solutions, Springer 2006
Module Examination:Final Module Examination (MAP)
Assessment Mode for Module Examination:
  • Written examination, 90 min. OR
  • Oral examination, 30-45 min. (with small number of participants)
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: Financial Mathematics in Continuous Time
  • Accompanying exercise
  • Related examination
Components to be offered in the Current Semester:
  • no assignment