Stochastic Analysis
Stochastische Analysis
8 CPirregularlyEN
Prerequisites
Recommended, as written
Knowledge of the content of the modules • 11217 : Wahrscheinlichkeitstheorie • 13889 : Stochastic Processes
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)
Learning outcomes
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.
Assessment
• 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.
Literature (5)
- 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.
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
Source: BTU's module description · retrieved 29 Sep 2026Original