Opening Lecture: The Early Days of Optimal Stopping
[Professor J. Laurie Snell, Dartmouth College, USA]

Course 1: General Theory of Optimal Stopping
[Professor Albert N. Shiryaev, Steklov Mathematical Institute, Moscow]
The course will provide a quick introduction to the general theory of optimal stopping, starting with key motivations and examples, and ending with the main results of modern theory being thoroughly explained. Both martingale and Markovian approaches will be considered in both discrete and continuous time. Relevant parts of martingale theory and the theory of Markov processes (including stochastic calculus) will be reviewed. Applications in financial mathematics (option pricing), mathematical statistics (sequential testing, quickest detection), and stochastic analysis (sharp inequalities) will be addressed.

Course 2: Optimal Stopping and Free-Boundary Problems
[Professor Goran Peskir, School of Mathematics, Manchester]
The course will focus on explaining the fundamental connection between optimal stopping problems (in probability) and free-boundary problems (in analysis). The setting will be Markovian, and apart from classic problem formulations due to Lagrange, Mayer and Bolza, the course will also deal with more recent problem formulations based on the maximum functional (the maximality principle). Recent advances in solving free-boundary problems in terms of nonlinear integral equations using the so-called ``local time-space calculus'' will be explained. Examples of application will include American/Asian options and optimal prediction problems (both of interest in financial mathematics).

Course 3: Methods of Solution
[Professor Lawrence A. Shepp, Rutgers University, USA]
The course will present various methods for solving optimal stopping problems. This will include the principle of smooth fit, the method of space change, the method of time change, and the method of measure change, as well as a general philosophy on the development of heuristics. The setting will be Markovian. Examples of application will include Russian options as well as other path-dependent options in financial markets. Long-standing open problems will be presented and discussed.

Guest Lecture 1: Optimal Stopping Problems for Random Walks and Lévy Processes
[Professor Alexander A. Novikov, University of Technology, Sydney]

Guest Lecture 2: Some Examples of Stochastic Games Driven by Brownian Motion
[Dr Andreas E. Kyprianou, Heriot-Watt University, Edinburgh]