Course syllabus

Course syllabus for Basic stochastic processes and financial applications

The course syllabus contains changes
See changes

Course syllabus adopted 2023-02-08 by Head of Programme (or corresponding).

Overview

Swedish name:
Grundläg­gande stokastiska processer och finansiella tillämp­ningar
Code:
MVE172
Credits:
7.5 Credits
Owner:
TKIEK
Education cycle:
Second-cycle
Main field of study:
Mathematics
Department:
MATH­E­MAT­I­CAL SCIENCES
Grading:
TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language

    English

  • Application code

    51117

  • Open for exchange students

    Yes

  • Only students with the course round in the programme overview.

Credit distribution

Module
Sp1
Sp2
Sp3
Sp4
Summer
Not Sp
Examination dates
0120 Laboratory 3 c
Grading: UG		 3 c
0220 Examination 4.5 c
Grading: TH		 4.5 c
  • 11 Jan 2027 pm J
  • 31 Mar 2027 am J
  • 19 Aug 2027 am J

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements

Course specific prerequisites

Sannolikhetsteori motsvarande en första kurs i matematisk statistik. Någon erfarenhet av datoranvändning såsom exempelvis grunderna i Matlab-programmering eller liknande. Matematikkunskaper motsvarande vad som läres ut under första året på I-linjen.

The equivalent of the course MVE095 Options and Mathematics.

Aim

Kursen syftar till att ge en introduktion till samt översikt av de klasser av stokastiska processer som är viktigast i såväl tekniska och naturvetenskapliga tillämpningar som i vidare matematisk och matematisk statistisk teoribyggnad.

Learning outcomes (after completion of the course the student should be able to)

  • narrate the theory for discrete time Markov chains and make applied calculations for them
  • narrate the meaning of dependence and independence between different stochastic process values/random variables and use this in applied calculations
  • narrate the defining properties of weak/wide sense stationary processes redogöra för de grundläggande definierande egenskaperna för svagt stationära processer, Gaussian/normal processes and martingales and make applied calculations for them
  • use stochastic processes as models in mathematical finance, e.g., to calculate prices for financial contracts/options

Content

Short repetition/treatment of some important concepts from mathematics and multivariate probability theory. Discrete time and continuous time stochastic processes. Finite dimensional distribution functions. Mean and autocorrelation/aoutocovariance function. Stationary and weak/wide sense stationary processes. Processes with independent stationary increments/Levy processes. Gaussian/normal processes. Discrete time Markov chains. Martingales in discrete and continuous time. Continuity for and differentiation, integration and summation of stochastic processes. Basic queueing theory. Computer implementation of most of the mentioned classes of stochastic processes. Finacial applications.

Organisation

Lectures, exercise sessions and computer laborations.

Literature

Hwei Hsu: Schaum's Outline of Probability, Random Variables, and Random Processes, Fourth Edition, 2019. ISBN 9781260453812

Examination including compulsory elements

Written exam. Mandatory computer laboration and presentation.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.

The course syllabus contains changes

  • Changes to course:
    • 2026-04-20: Litterature Litterature changed by UBS/Viceprefekt
      Updated literature