NMAK16015U Optimal Stopping with Applications
MSc Programme in Actuarial Mathematics
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.
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.
1. Sequential hypothesis testing.
2. Quickest detection problems in technical analysis of financial data.
The content of the course.
- 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
Optimal stopping theory and applications to finance or life insurance
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
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.
There will be provided feedback during the course based on exercises at the lectures.
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- 7,5 ECTS
- Type of assessment
- Oral examination
- Type of assessment details
- 20-minute oral exam without time for preparation
- Without aids
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners.
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 code
- 7,5 ECTS
- Full Degree Master
- 1 block
- Block 2
- Course capacity
- No limit
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Jesper Lund Pedersen (6-6e6977746976447165786c326f7932686f)