The following gives a brief breakdown of the main areas of activity for the Symposium.

1. General theory of optimal stopping
The opening morning lecture will be given by E. Snell who will speak on his fundamental discovery from 1952 (Snell's envelope). Remaining talks in the morning will be devoted to the martingale approach to optimal stopping both in discrete and continuous time. The opening afternoon lecture was to be given by E. Dynkin who was to speak on his fundamental discovery from 1963 (superharmonic characterization). Remaining talks in the afternoon will be devoted to the Markovian approach to optimal stopping both in discrete and continuous time. Continuous time problems will be tackled using general techniques including variational inequalities. Discrete time problems are subject to a number of additional mathematical curiosities over and above what one may experience for continuous time models. Combinatorial aspects and techniques based around discrete probability will be exposed in both morning and afternoon sessions. This will include reviews and extensions of classical problems such as the parking problem, secretary-type problems, and problems involving sequences of independent indicators for example. 

2. Optimal stopping and free boundary problems
The connection between optimal stopping problems and free-boundary problems in mathematical physics (the obstacle problem and the Stefan problem describing the process of melting and solidification) raises many challenging questions to analysts when the underlying Markov process has jumps (such as Lévy processes). In this case one needs to deal with PIDEs (instead of PDEs) and very little is known about regularity of the fundamental solution. On the other hand, the methods relying upon local-time calculus allow an approach to the problem via nonlinear integral equations for the optimal boundary so that existence and uniqueness results can still be proved. This line of research is very promising but still needs to be fully developed. Principally, this day will be devoted to the issue of stochastic representation which lies at the heart of the relationship between free boundary problems and optimal stopping problems. The morning will be devoted to probabilistic/analytical methods and the afternoon to numerical methods. Special attention will be given to PDEs and PIDEs solved by the value function. This will include modern methods such as randomization of time horizons, viscosity solutions, as well as more classical methods of analysis including variational inequalities. In addition, characterizations of optimal stopping boundaries (via nonlinear integral equations for example) will play an important role. Issues such as their smoothness and asymptotic behaviour will be brought to light. 

3. Methods of solution
As optimal stopping theory may not necessarily be considered as a categorical theory, quite often one finds that the extent to which a technique may be used only extends to a limited class of problems. On this day speakers will offer an assortment of problems in which different probabilistic techniques have been applied offering access to solutions to different classes of problems. In addition to exposing ad-hoc methods, the aim of the talks will also be to expose principles which can be found common to all optimal stopping problems. Topics will include the following. 

(1) The principles of smooth and continuous fit. Recent advances in clarification of the two most useful analytic facts are to be exposed. Illuminating discussions on this topic are anticipated. 

(2) The maximality principle. The intriguing problem is to examine under what conditions this principle remains valid for Markov processes with jumps. Some of the recent work has focused on clarifying this issue in some special cases of Lévy processes. 

(3) Fluctuation theory of Lévy processes and applications to optimal stopping. Many solutions to optimal stopping problems boil down to a first passage problem of an underlying Markov process. The recent advances in the theory of Lévy processes, and in particular fluctuation theory, has also provided a cache of knowledge offering new possibilities for solving optimal stopping problems driven by Lévy processes. 

(4) Stochastic analysis and sharp inequalities. The most challenging problem remains to determine the best constant in the classic Burkholder-Davis-Gundy inequality. Some recent progress in this direction is to be disclosed. 

4. Applications I (Financial Mathematics)
The aim of this day will be to expose three main applications of optimal stopping in financial mathematics. 

(1) A number of recent contributions to the pricing of American type options in Black-Scholes and other semi-martingale markets (in particular Lévy driven markets) will be exposed. Examples of such options include the classical American put (for which new results are still being established), Russian options, Asian options, Integral options, Bermudan options and so on. Attention will be drawn to accurate characterizations of optimal exercise boundaries, early exercise decompositions, and associated free boundary problems. 

(2) Credit risk has recently shown that the issue of establishing endogenous default levels for the equity of a firm boils down to understanding a particular class of optimal stopping problems. This most recent direction and its intimate relationship with smooth and continuous fit principles will be considered. 

(3) Game type options are a natural extension of American type options. These are options in which both writer and seller have the right to exercise, each resulting in a pay out for the holder. The writer's objective to minimize the payout and the holder to maximize. A number of recent examples of such options have been considered both with finite and infinite time horizons. Results in this direction as well as the many challenges that lay ahead will be presented here. 

5. Applications II (Sequential Analysis)
The aim of this day will be to focus on the following topics: 

(1) Sequential testing. The old problem of testing three simple hypotheses still remains unsolved. It is hoped that the recent advances in characterizing the optimal boundaries as unique solutions of nonlinear integral equations may be helpful in tackling the problem. 

(2) Quickest detection. Recent applications involve a quickest detection of arbitrage. A significant progress in understanding the problem is achieved for Markov processes with jumps and the exchange of facts and ideas in this direction will be most stimulating and useful. 

(3) Optimal prediction. This is a new problem formulation in continuous time where the underlying gain process is not adapted. Recently developed techniques to solve problems of this type are to be exposed. New optimal prediction problems are to be formulated. These problems appear useful in diverse applications, most notably in financial mathematics and financial engineering.