ELE 3917 Stochastic Processes for Finance and Economics
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.
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.
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.
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.
- Random Variables
- Conditional probability and conditional expectation
- Exponential distribution and Poisson processes
- Discrete random walks
- Brownian motion (continuous random walk)
- Applications in finance and economics
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
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.
Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.
MET 2910 / EXC 2910 Mathematics, ELE 3776 Mathematical Analysis (or equivalent). Prior knowledge of ELE3776 Mathematical Analysis is also recommended, but not a requirement.
|Exam category||Weight||Invigilation||Duration||Support materials||Grouping||Comment exam|
Form of assessment:
Examination when next scheduled course
|100||Yes||3 Hour(s)||Individual||Final exam|
|Form of assessment:||Written submission|
|Support materials:|| |
|Exam code:||ELE 39171|
|Resit:||Examination when next scheduled course|
Prepare for teaching
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.