Optimal Stopping with Applications

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