Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)
Stochastic Processes Applied to Financial Models, 6 credits
Stokastiska processer för finansmarknadsmodeller, 6 hp
TAMS29
Main field of study
Mathematics Applied MathematicsCourse level
Second cycleCourse type
Programme courseExaminer
Jörg-Uwe LöbusDirector of studies or equivalent
Ingegerd SkoglundEducation components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
Second cycleAdvancement level
A1XCourse offered for
- Industrial Engineering and Management - International, M Sc in Engineering
- Industrial Engineering and Management, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Mathematics, Master's programme
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
Entry requirements
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.
Prerequisites
Linear Algebra, Analysis. Introduction to Probability Theory. A second course in mathematical analysis is useful.Intended learning outcomes
The course gives an introduction to the theory of stochastic processes and the Black-Scholes model. After a completed course the student is expected to be able to:
- handle advanced items and theorems within the theory of stochastic processes, such as the Kolmogorov extension theorem, ergodicity of time discrete Markov chains, the Kolmogorov differential equations for time continuous Markov chains, Wiener process, Ornstein-Uhlenbeck process, stochastic Itô-integral, Itô-formula, Martingales in discrete and continuous time Doleans measure and stopping
- construct solutions to stochastic differential equations
- understand the two different approaches to the Black-Scholes formula, on the one hand by means of the geometric Brownian motion and related partial differential equations, on the other hand by means of the fundamental theorem of pricing
- calculate the fair price of certain financial assets
Course content
Martingales, Markov processes, stochastic integrals, stochastic differential equations, Brownian motion, Itô's formula, Girsanov's theorem,
diffusion processes, random walk, Ising model,
Black-Scholes formula, risk-neutal valuation, volatility,
geometric Brownian motion and statistical analysis of stock prices,Teaching and working methods
Lectures and tutorials.
Examination
TEN1 Written Examination 6 credits U, 3, 4, 5 Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Jörg-Uwe LöbusCourse website and other links
http://courses.mai.liu.se/GU/TAMS29Education components
Preliminary scheduled hours: 48 h
Recommended self-study hours: 112 h
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | Written Examination | 6 credits | U, 3, 4, 5 |
Regulations (apply to LiU in its entirety)
The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.
LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.
Course literature is preliminary.
There is no course literature available for this course in studieinfo.
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
X
|
X
|
X
|
|||
| 1.2 Fundamental engineering knowledge (G1X level) |
|
|
|
|||
| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
X
|
|
|
|||
| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
|
|
|
|||
| 1.5 Insight into current research and development work |
|
|
|
|||
| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
X
|
X
|
X
|
|||
| 2.2 Experimentation, investigation, and knowledge discovery |
X
|
X
|
X
|
|||
| 2.3 System thinking |
|
|
|
|||
| 2.4 Attitudes, thought, and learning |
|
X
|
|
|||
| 2.5 Ethics, equity, and other responsibilities |
|
X
|
|
|||
| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
|
|
X
|
|||
| 3.2 Communications |
|
|
X
|
|||
| 3.3 Communication in foreign languages |
|
|
X
|
|||
| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
|
|
|
|||
| 4.2 Enterprise and business context |
|
|
|
|||
| 4.3 Conceiving, system engineering and management |
|
|
|
|||
| 4.4 Designing |
|
|
|
|||
| 4.5 Implementing |
|
|
|
|||
| 4.6 Operating |
|
|
|
|||
| 5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS | ||||||
| 5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development |
|
|
|
|||
| 5.2 Economic conditions for knowledge development |
|
|
|
|||
| 5.3 Identification of needs, structuring and planning of research or development projects |
|
|
|
|||
| 5.4 Execution of research or development projects |
|
|
|
|||
| 5.5 Presentation and evaluation of research or development projects |
|
|
|
|||
This tab contains public material from the course room in Lisam. The information published here is not legally binding, such material can be found under the other tabs on this page.
There are no files available for this course.