Recommended prerequisite for participation in the module

The module builds on knowledge obtained by the modules Linear Algebra with Applications, Analysis 1, Analysis 2, and Probability Theory.

Content, progress and pedagogy of the module

Learning objectives

Knowledge

• know how to rigorously formulate concepts from probability theory by means of measure and integration theory, in particular, how to express information through sigma-algebras and how to define and employ conditional expectations
• know about stochastic processes in discrete and continuous time
• know about Wiener processes
• know about martingales
• know about stochastic integrals, Itô’s formula and Girsanovs theorem

Skills

• are able to understand and apply the rules of Itô's stochastic calculus
• are able to conduct a change of measure for a martingale

Competences

• are able to formulate mathematical results in a correct manner by means of measure-theoretical and probabilistic argumentation
• are able to apply and mediate basic mathematics and theory related to stochastic processes
• able to gain additional knowledge regarding probability theoretical subjects related to stochastic processes and their application in finance

Type of instruction

As described in §17 in the curriculum. 

Extent and expected workload

This is a 5 ECTS project module and the work load is expected to be 150 hours for the student.

Exam

Exams

Name of exam	Stochastic Analysis
Type of exam	Written or oral exam
ECTS	5
Assessment	Passed/Not Passed
Type of grading	Internal examination
Criteria of assessment	The criteria of assessment are stated in the Examination Policies and Procedures