Stochastic Calculus and Its Applications


Recommended prerequisite for participation in the module

The module builds on knowledge and skills obtained in the module Stochastic Analysis. Experience with programming in R is expected. Previous knowledge of models in financial mathematics is helpful but not necessary.

Content, progress and pedagogy of the module

Students who have completed the module will gain knowledge of the theoretical background for stochastic integration as well as its application to finance.

Learning objectives


  • Know about stochastic integration with respect to continuous semimartingales
  • Know about the quadratic variation of stochastic integrals
  • Know about Itô’s formula
  • Know about change of measures via Girsanov’s Theorem with special emphasis on its use in arbitrage theory
  • Know about Stochastic Differential Equations (SDE’s) and its relevance in the modelling of asset prices
  • Know how to solve SDE’s numerically


  • Are able to apply basic computation rules and calculi associated to stochastic integrals
  • Are able to apply Itô’s formula
  • Are able to conduct a change of measure via Girsanov’s Theorem
  • Can apply basic methods of stochastic calculus to the modelling of financial markets
  • Are able to solve SDE’s theoretically and numerically


  • Are able to read, understand, criticize and make use of advanced literature on stochastic calculus
  • Are able to connect, formulate, and analyze scientific problems with the basic theory of stochastic integration

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.



Name of examStochastic Calculus and Its Applications
Type of exam
Written or oral exam
Permitted aidsDer henvises til den pågældende semesterbeskrivelse/modulbeskrivelse
AssessmentPassed/Not Passed
Type of gradingInternal examination
Criteria of assessmentThe criteria of assessment are stated in the Examination Policies and Procedures

Facts about the module

Danish titleStokastisk kalkule med anvendelser
Module code23KMØK2STOCA
Module typeCourse
Duration1 semester
Language of instructionDanish and English
Location of the lectureCampus Aalborg
Responsible for the module


Study BoardStudy Board of Mathematical Sciences
DepartmentDepartment of Mathematical Sciences
FacultyThe Faculty of Engineering and Science