Forudsætninger/Anbefalede forudsætninger for at deltage i modulet

The module builds on knowledge obtained by the modules Linear Algebra with Applications, Analysis 1, Analysis 2, and Probability Theory from the BSc in Mathematics-Economics.

Modulets indhold, forløb og pædagogik

Læringsmål

Viden

• 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

Færdigheder

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

Kompetencer

• 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

Undervisningsform

As described in the introduction to Chapter 3.

Omfang og forventet arbejdsindsats

Module duration is 5 ECTS equivalent to a workload of 137,5 hours.
 

Eksamen

Prøver

Prøvens navn	Measure Theory and Stochastic Processes
Prøveform	Skriftlig eller mundtlig
ECTS	5
Bedømmelsesform	Bestået/ikke bestået
Censur	Intern prøve
Vurderingskriterier	Vurderingskriterierne er angivet i Universitetets eksamensordning

Yderligere informationer

Please contact Study Board of Mathematical Sciences - studyboard@math.aau.dk