Optimal Stopping and Applications

Contact us

• Alex Cox

• Andreas Kyprianou

Notes

• Theory Notes (Lectures 1-5)
• American Options (Lecture 9)

This graduate course aims to provide an introduction to the theory and practice of optimal stopping. Optimal stopping questions arise in a number of practical and theoretical situations, wherever there is the need to make a single, irreversible decision under uncertain knowledge of the future. Applications of the theory arise in statistics, mathematical finance and stochastic analysis. The study of optimal stopping problems leads to connections with free-boundary problems.

The course will roughly follow the treatment given in the book Optimal Stopping and Free-Boundary Problems by Peskir and Shiryaev. There is a copy of this book in the library (currently on order), and from campus one can access the book electronically. A reasonable level of comfort with continuous-time processes and stochastic integration will be assumed, although many techniques and ideas will be introduced as encountered.

UPDATED: The course is timetabled at **13.15-15.05** on Tuesdays in 1W3.20a. An approximate outline of the lectures is as follows:

Lecture 1 (27/1/09)

Introduction; Motivation; Optimal Stopping problems in discrete time

Lecture 2 (3/2/09)

Optimal Stopping problems in discrete time; Martingale approach; Markovian Approach

Lecture 3 (10/2/09)

Optimal Stopping problems in continuous time; Martingale approach

Lecture 4 (17/2/09)

Optimal Stopping problems in continuous time - Markovian Approach

Lecture 5 (24/2/09)

Free-boundary problems and optimal stopping

Lecture 6 (3/3/09)

(Andreas Kyprianou) Smooth fit & continuous fit

Lecture 7 (10/3/09)

(Andreas Kyprianou) Example: Lévy processes

Lecture 8 (17/3/09)

(Juan Carlos Pardo Millan) The Gapeev-Kühn stochastic game driven by spectrally positive Lévy processes.

Lecture 9 (24/3/09)

(Martin Herdegen) Example: Mathematical Finance - The American Put

Lecture 10 (21/4/09)

Example: Optimal stopping of the maximum

It is expected/hoped that some volunteers will prepare some of the later lectures, and the list will be updated as the semester progresses.

Related Information

• Prob-L@b

• Informal Probability seminars

• About our Research in Probability

• Subscribe to the prob-sem mailing list to receive details of activities within the probability group