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ELE 3917 Stochastic Processes for Finance and Economics

ELE 3917 Stochastic Processes for Finance and Economics

Course code: 
ELE 3917
Department: 
Economics
Credits: 
7.5
Course coordinator: 
Fabian Harang
Course name in Norwegian: 
Stochastic Processes for Finance and Economics
Product category: 
Bachelor
Portfolio: 
Bachelor - Programme Electives
Semester: 
2023 Spring
Active status: 
Active
Level of study: 
Bachelor
Teaching language: 
English
Course type: 
One semester
Introduction

Stochastic processes play a fundamental role in modeling of uncertain phenomena in business and economics. They are today used in a great variety of models to both understand risk associated with investments and to make better decisions when faced with uncertain, or seemingly random, parameters.  Typical application areas include valuation of financial assets, pricing of insurance products, interest rate forecasting, business simulation analysis, optimization under uncertainty and control theory.

Learning outcomes - Knowledge

The students will be introduced to various discrete and continuous time stochastic processes, which frequently appear in financial and economic modeling. They will learn how these stochastic processes are applied in practical problems, and will understand how basic tools from statistics and mathematics can be used to analyse them. Through elementary examples relating to gambling and finance, the students will see how stochastic processes can be used to understand and solve real problems.

Learning outcomes - Skills

After completion of the course, the student will: 

  • Have a good understanding of discrete and continuous random variables, expectation and conditional expectation, as well as moments of random variables. 
  • Be familiar with Poisson processes and discrete random walks
  • Understand the relation between a discrete random walk and the continuous Brownian motion.
  • Be able to provide an elementary analysis of the sample paths of stochastic processes.
  • Have developed a mathematical toolbox for the analysis of stochastic processes. 
  • Be able to simulate elementary stochastic processes using R or Matlab. 
  • Be aware of how these models are applied in economics, insurance and finance.
  • Be able to create simple models for gambling and insurance by using Monte Carlo simulations.
General Competence

Students will work throughout the semester with various written assignments, which in the end will be evaluated and part of the final grade. Students are allowed to collaborate on the assignments, and half way through the semester get the chance to give an oral presentation of their results and receive feedback.

Oral presentations of mathematical computations and ideas is an important skill valued by employers in the industry and will prove useful for further studies.

Course content
  1. Random Variables
  2. Conditional probability and conditional expectation
  3. Exponential distribution and Poisson processes
  4. Discrete random walks
  5. Brownian motion (continuous random walk)
  6. Applications in finance and economics
  7. Simulations
Teaching and learning activities

The course will be thought on campus, as well as through asynchronous videos posted on its learning. In main part, the main curriculum will be presented through online videos, while the physical lectures will be used for discussion, exercises and peer interactions. The students are expected to watch the videos with the course curriculum each week before attending the physical lecture where the curriculum will be discussed

This is a course with continuous assessment (several exam components) and one final exam code. Each exam component is graded by using points on a scale from 0-100. The components will be weighted together according to the information in the course description in order to calculate the final letter grade for the examination code (course). Students who fail to participate in one/some/all exam elements will get a lower grade or may fail the course. 

During the semester, students will work on various written assignments, either individually or in collaboration with a fellow student, and will get the chance to get feedback on the assignments during a mid-term voluntary oral presentation. The collection of the assignments will be evaluated and graded in the end of the semester, and the grade on this collection will count 40% of the final grade. There will be a final written exam in the end of the semester which counts for 60% of the grade. 

Software tools
Matlab
R
Qualifications

Higher Education Entrance Qualification

Disclaimer

Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.

Required prerequisite knowledge

MET 2910 / EXC 2910 Mathematics, ELE 3776 Mathematical Analysis (or equivalent)

Exam categoryWeightInvigilationDurationSupport materialsGroupingComment exam
Exam category:
Submission
Form of assessment:
Written submission
Exam code:
ELE 39171
Grading scale:
Point scale leading to ECTS letter grade
Grading rules:
Two examiners
Resit:
All components must, as a main rule, be retaken during next scheduled course
40No1 Semester(s)Group/Individual ( 1 - 2)Students will get the chance to present their working assignment in class and get feedback before submission.
Exam category:
Submission
Form of assessment:
Written submission
Exam code:
ELE 39171
Grading scale:
Point scale leading to ECTS letter grade
Grading rules:
Two examiners
Resit:
All components must, as a main rule, be retaken during next scheduled course
60Yes5 Hour(s)
  • BI-approved exam calculator
  • Simple calculator
  • Bilingual dictionary
Individual Final exam
Exams:
Exam category:Submission
Form of assessment:Written submission
Weight:40
Invigilation:No
Grouping (size):Group/Individual (1-2)
Support materials:
Duration:1 Semester(s)
Comment:Students will get the chance to present their working assignment in class and get feedback before submission.
Exam code:ELE 39171
Grading scale:Point scale leading to ECTS letter grade
Resit:All components must, as a main rule, be retaken during next scheduled course
Exam category:Submission
Form of assessment:Written submission
Weight:60
Invigilation:Yes
Grouping (size):Individual
Support materials:
  • BI-approved exam calculator
  • Simple calculator
  • Bilingual dictionary
Duration:5 Hour(s)
Comment: Final exam
Exam code:ELE 39171
Grading scale:Point scale leading to ECTS letter grade
Resit:All components must, as a main rule, be retaken during next scheduled course
Type of Assessment: 
Continuous assessment
Grading scale: 
ECTS
Total weight: 
100
Student workload
ActivityDurationComment
Teaching
45 Hour(s)
Prepare for teaching
75 Hour(s)
Examination
5 Hour(s)
Final written exam
Seminar groups
75 Hour(s)
Sum workload: 
200

A course of 1 ECTS credit corresponds to a workload of 26-30 hours. Therefore a course of 7,5 ECTS credit corresponds to a workload of at least 200 hours.