NMAK16015U Optimal Stopping with Applications
MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economics
The theory of optimal stopping is concerned with the problem of choosing a time to take a particular action. Some applications are:
- The valuation/pricing of financial
products/contracts, where the holder has the right to exercise
the contract at any time before the date of expiration is
equivalent to solving optimal stopping problems.
Examples:
1. American options in finance
2. Surrender options in life insurance
3. Prepayment of mortage loans - In financial engineering, where the problem is to
determine an optimal time to sell an asset. Examples:
1. Optimal prediction problem, to sell the asset when the price is, or close to, the ultimate maximum.
2. Mean-variance stopping problem, to sell the asset so as to maximise the return and to minimise the risk. - In mathematical statistics, where the sample size is unknown.
Examples:
1. Sequential hypothesis testing.
2. Quickest detection problems in technical analysis of financial data.
The content of the course.
Optimal stopping:
- Definitions
- General theory
- Methods of solutions and numerical methods
Areas of applications:
- Pricing financial products with exercise feature in mathematical finance or life insurance
- Financial engineering
- Mathematical statistics
Knowledge:
Optimal stopping theory and applications to finance or life insurance
Skills:
At the end of the course, the students are expected to be able to
- Apply general theory of optimal stopping
- Apply methods for solutions of examples of optimal stopping
- Pricing American derivatives
- Apply optimal stopping methods in mathematical statistics
Competences:
To make the student operational and to give the student knowledge in applications of optimal stopping in finance or life insurance
Book and articles
Academic qualifications equivalent to a BSc degree is recommended.
- Category
- Hours
- Lectures
- 28
- Preparation
- 177
- Exam
- 1
- Total
- 206
There will be provided feedback during the course based on exercises at the lectures.
- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination
- Type of assessment details
- 20-minute oral exam without time for preparation
- Aid
- Without aids
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners.
- Re-exam
As the ordinary exam.
Criteria for exam assesment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Course information
- Language
- English
- Course code
- NMAK16015U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- B
- Course capacity
- No limit
Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Jesper Lund Pedersen (jesper@math.ku.dk)