# NMAK16015U Optimal Stopping with Applications

Volume 2023/2024
Education

MSc Programme in Actuarial Mathematics

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.
• 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

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 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

Continuous time finance

Academic qualifications equivalent to a BSc degree is recommended.
4 hours of lectures per week for 7 weeks
Identical to NMAK16015U Optimal Stopping with Applications.
• Category
• Hours
• Lectures
• 28
• Preparation
• 177
• Exam
• 1
• Total
• 206
Continuous feedback during the course of the semester

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.