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Optimal Stopping with Applications
Provider: Faculty of Science

Activity no.: 5612-19-07-31 
Enrollment deadline: 01/09/2019
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time02.09.2019, at: 09:00 - 10.11.2019, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserJesper Lund Pedersen    E-mail address: jesper@math.ku.dk
Written languageEnglish
Teaching languageEnglish partially in English
Semester/BlockBlock 1
Scheme groupB
Exam formOral examination, 30 min. Without time for preparation
Exam formOral examination
Exam detailsThe 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.
Course workload
Course workload categoryHours
Lectures28.00
Preparation177.00
Exam1.00
Sum206.00
Content
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.

The content of the course.
Optimal stopping:
- Definitions
- General theory
- Methods of solutions

Areas of applications:
- Pricing financial products with exercise feature in mathematical finance or life insurance
- Financial engineering

Learning outcome
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 option

Competences:
To make the student operational and to give the student knowledge in applications of optimal stopping in finance or life insurance

Literature
Book and articles

Teaching and learning methods
4 hours of lectures per week for 7 weeks

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