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 selected topics concerning general measure theory with
special focus on probability theoretical. Topics as existence and
uniqueness of measures, Lebesgue-integration, Expectation and
condition expectation, Radon-Nikodyms theorem, and information
expressed through sigma-algebras
- know about stochastic processes in discrete and continuous
time
- know about Wiener processes
- know about Martingales
- know about stochastic integrals, Ito’s formula and Girsanovs
theorem
Færdigheder
- are able to calculate fundamental characteristics for
stochastic processes.
- 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
Kursusmodulets omfang er 5 ECTS svarende til 150 timers
studieindsats.
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 |