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.
The content of the course.
- General theory
- Methods of solutions
Areas of applications:
- Pricing financial products with exercise feature in mathematical finance or life insurance
- Financial engineering
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 option
To make the student operational and to give the student knowledge in applications of optimal stopping in finance or life insurance
Book and articles
- 7,5 ECTS
- Type of assessment
- Oral examination30-minute oral exam without time for preparation
The student may bring notes to the oral exam, but they are only allowed to consult these in the first minute after they have drawn a question. After that, all notes must be put away.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners.
As the ordinary exam.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.