Course syllabus for Basic stochastic processes and financial applications

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

Overview

  • Swedish nameGrundläggande stokastiska processer och finansiella tillämpningar
  • CodeMVE172
  • Credits7.5 Credits
  • OwnerTKIEK
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 51114
  • Open for exchange studentsYes
  • Only students with the course round in the programme overview.

Credit distribution

0120 Laboratory 3 c
Grading: UG		0 c3 c0 c0 c0 c0 c
0220 Examination 4.5 c
Grading: TH		0 c4.5 c0 c0 c0 c0 c
  • 07 Dec 2024 am J
  • 14 Apr 2025 am J
  • 19 Aug 2025 pm 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 above.

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 above.

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: Probability, Random Variables, and Random Processes, 2nd Edition. Schaum's Outlines, McGraw-Hill 2010. Lecture notes on financial applications.

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 on educational support due to disability.