Multiple Stopping Problems

This book presents the theory of rational decisions involving the selection of stopping times in observed discrete-time stochastic processes, both by single and multiple decision-makers. Readers will become acquainted with the models, strategies, and applications of these models.

It begins with an examination of selected models framed as stochastic optimization challenges, emphasizing the critical role of optimal stopping times in sequential statistical procedures. The authors go on to explore models featuring multiple stopping and shares on leading applications, particularly focusing on change point detection, selection problems, and the nuances of behavioral ecology. In the following chapters, an array of perspectives on model strategies is presented, elucidating their interpretation and the methodologies underpinning their genesis. Essential notations and definitions are introduced, examining general theorems about solution existence and structure, with an intricate analysis of optimal stopping predicaments and addressing crucial multilateral models. The reader is presented with the practical application of models based on multiple stopping within stochastic processes. The coverage includes a diverse array of domains, including sequential statistics, finance, economics, and the broader generalization of the best-choice problem. Additionally, it delves into numerical and asymptotic solutions, offering a comprehensive exploration of optimal stopping quandaries.

The book will be of interest to researchers and practitioners in fields such as economics, finance, and engineering. It could also be used by graduate students doing a research degree in insurance, economics or business analytics or an advanced undergraduate course in mathematical sciences.

Georgy Sofronov received his PhD degree in Probability Theory and Mathematical Statistics from Moscow State University in 2002. He has held academic positions at several universities including the University of Queensland and the University of Wollongong. Currently, he is an Associate Professor in Statistics at Macquarie University. He serves on the editorial boards of Statistical Papers and Methodology and Computing in Applied Probability. His research interests include Markov chain Monte Carlo simulation, the Cross-Entropy method, change-point problems and optimal stopping rules.

Krzysztof J. Szajowski received his PhD degree and habilitation in Mathematical Sciences from the Technical University of Wrocław in 1980 and 1996, respectively. Since 1973, he has held academic and visiting research positions at Wroclaw University of Technology, Delft University of Technology, Purdue University and the Institute of Mathematics of the Polish Academy of Sciences. Currently, he is an Emeritus Professor at Wroclaw University of Science and Technology. He is a member of the editorial board of Mathematica Applicanda and former its editor-in-chief, as well as a member of the editorial board of the journal Scientiae Mathematicae Japonicae and Annals of Dynamic Games. His current research interests lie in probability theory and mathematical statistics, applied mathematics, change-point detection, optimal stopping problems and game theory models.