Optimal stopping with applications: an editorial introduction

This special issue of Stochastics contains selected papers based on the talks given at the symposium ‘Optimal Stopping with Applications’ that was held from 23 to 26 June 2009 at Åbo Akademi University in Turku/Åbo, Finland.

This issue has been edited by the Editor-in-chief (Saul Jacka) and the two guest editors (Goran Peskir and Paavo Salminen). All the papers have undergone a full refereeing process. The editors would like to thank all the participants as well as the authors and referees for contributing to the success of the symposium and this special issue.

The symposium should be seen as the follow-up to the symposium held in January 2006 in Manchester in the UK. Selected papers from the Manchester symposium were published in Stochastics, Vol. 79, Nos. 1–4 (2007).

The symposium was made possible by financial assistance from the European Science Foundation (via the network Advanced Mathematical Methods in Finance), Åbo Akademi University, the Turku School of Economics, the Magnus Ehrnrooth Foundation, the Federation of Finnish Learned Societies and the Research Institute Foundation of Åbo Akademi University (Stiftelsens för Åbo Akademi forskningsinstitut).

The programme of the symposium included 20 invited talks and as well as 28 contributed talks. There were 77 participants from 19 different countries. Among the participants, there were 20 PhD students, 27 younger researchers and 30 more senior researchers.

An important application of the theory of optimal stopping lies in the pricing of American options. About half of the talks were concerned with or motivated by problems in finance, insurance and risk management. More generally, the talks presented at the symposium could be divided into the following subgroups of the theory and applications of optimal stopping:

•	theoretical developments;
•	applications in mathematical statistics;
•	choosing the best object;
•	detection problems;
•	applications in mathematical finance and insurance;
•	gambling applications and
•	other applications.

The symposium was very successful in both its scientific and social aspects. Many of the world-leading specialists attended the meeting. There were lively discussions between the participants and the speakers. The programme managed to offer a very wide view of the state of the art of the theory and applications of optimal stopping, and this is reflected in the contents of this special issue of Stochastics.

A list of the talks presented at the symposium (arranged alphabetically by author) is as follows.

Alvarez, Luis H. R.: A class of solvable optimal stopping problems of spectrally negative jump diffusions.

Ano, Katsonori: Optimal stopping problem with uncertain stopping and its application to discrete options.

Arkin, Vadim: A variational approach to an optimal stopping and free-boundary problems.

Baurdoux, Erik: The Shepp–Shiryaev stochastic game driven by a spectrally negative Lévy process.

Bordag, Ljudmila: Study of the risk-adjusted pricing methodology model with methods of geometrical analysis.

Bouchard, Bruno: Optimal control under stochastic target constraints.

Bruss, F. Thomas: Optimal stopping with two types of constraints.

Christensen, Sören: On measure-changing-techniques for optimal stopping of diffusions.

Chudjakow, Tatjana: The best choice problem under ambiguity.

Dayanik, Savas: Compound Poisson disorder problems with non-linear detection delay penalty cost functions.

Delbaen, Freddy: Monetary time consistent utility functions.

Djehiche, Boualem: Stochastic impulse control for non-Markov processes.

Dolinsky, Yan: Applications of weak convergence for hedging of American and game options.

Du Toit, Jacques: A sojourn time problem for Brownian motion with drift.

Ekström, Erik: Optimal liquidation of a call spread.

Gapeev, Pavel V.: Some optimal stopping problems in models with partial information.

Glover, Kristoffer: Path-dependent British options.

Grigorescu, Ilie: Optimal strategy for the Vardi casino.

Helmes, Kurt: A linear programming method to derive optimal thinning strategies for classes of stochastic forest models.

Hobson, David: Recovering a time-homogeneous price process from perpetual option prices.

Kifer, Yuri: Perfect and partial hedging for multiple exercise (swing) game options.

Kyprianou, Andreas E.: General tax structures and the Lévy insurance risk model.

Lempa, Jukka: Optimal timing with Poisson clock.

Lerche, Hans Rudolf: Generalized parking problems.

Loeffen, Ronnie: De Finetti's dividend problem with absolutely continuous controls.

Ludkovski, Michael: A simulation approach to optimal stopping.

Lundgren, Robin: Optimal stopping and reselling of European options.

Matsumoto, Koichi: Simple improvement method for upper bound of American options.

Mazalov, Vladimir V.: Best-choice problem with disorder and imperfect information.

Meilijson, Isaac: The expected diameter of an L ²-bounded martingale is bounded from above by times the standard deviation of the last term.

Mikou, Mohammed: The smooth-fit principle of the American put price in the exponential Lévy model.

Nakai, Toru: Properties of a maintenance system on a partially observable Markov process and an optimal stopping problem.

Øksendal, Bernt: Singular stochastic control and optimal stopping with partial information.

Pardo, Juan Carlos: The Gapeev–Kühn stochastic game driven by a spectrally positive Lévy process.

Pasternak-Winiarski, Adam: Optimal stopping of a risk process in a continuous-time disorder model.

Pedersen, Jesper Lund: Some non-linear non-standard optimal stopping problems.

Peskir, Goran: The British put-call symmetry.

Presman, Ernst: Modification of Sonin's algorithm for optimal stopping of Markov chain.

Ramsey, David: Mutual mate choice with multiple criteria.

Rehman, Nasir: American foreign-exchange option in time-dependent one-dimensional diffusion model for exchange rate.

de Saporta, Benoite: Numerical method for optimal stopping of piecewise deterministic Markov processes.

van Schaik, Kees: On the McKean optimal stopping game driven by a spectrally negative Lévy process.

Shepp, Larry: How to gamble if you must (and if you really hate to gamble).

Shiryaev, Albert N.: On the optimal one-time rebalancing of the portfolio in the Black–Scholes model.

Sonin, Isaac: The optimal stopping of ‘seasonal’ observations and the game of ‘seasonal’ stopping.

Steinberg, Constantine: Continue, stop, restart probability model.

Stockbridge, Richard H.: A novel analysis of entry-and-exit investment decisions.

Szajowski, Krzysztof: On optimal stopping of risk process.

Villeneuve, Stephane: On the modelling of debt maturity and endogenous default: a caveat.

Vorbrink, Jörg: Exercise strategies for American exotic options under ambiguity.

Vostrikova, Ljudmila: Exponential Lévy models with change point.

Windridge, Peter: Minimising the time to a majority decision.

Xu, Mingxin: Infinite horizon optimal search problem with hiring and firing options.

Zervos, Mihail: π options.

Zhang, Cun-Hui: Primitive casinos in the presence of inflation.