About the Book
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.
Table of Contents:
Part 1: Preface on Multiple Stopping Models 1. Motivation for the Multiple Stopping and Selected Application Part 2: Multiple stopping and stopping games 2. Multiple optimal stopping rules 3. Multilateral multiple stopping: game theory approach Part 3: Applications of multiple stopping models 4. Sequential methods of statistics 5. Financial applications 6. The best choice problems 7. Numerical and asymptotic solutions for optimal stopping problems Part 4: Auxiliary & supplementary material
About the Author :
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.
Review :
“It is known that solutions to probabilistic problems should be well-understood in the discrete-time models first before the same problems should be studied in the related continuous-time models. The authors fulfilled the outstanding gap very successfully by providing an extensive literature source on the most generally formulated multiple stopping problems in the discrete-time case.”
–Pavel V. Gapeev, London School of Economics and Political Science, UK
“The book presents an encyclopaedic approach to optimization problems with multiple stopping times as the strategies. The book is unique, there is no such position in the literature. Multiple stopping times appear in a natural way in many human activities and frequently people are not aware of possibility of optimization among such strategies. The authors show a number of motivating applications of the developed theory in sequential methods of statistics, selection problems, investment (management) problems and in behavioural ecology. Reading the book substantial mathematical skills are not required. The book is written to general audience of decision makers and for researchers in mathematics, statistics, economics, engineering, operation research and business administration. In many problems exact solutions are presented. Numerical methods are also shown.”
- Łukasz Stettner, Institute of Mathematics Polish Acad. Sci.
"I highly recommend this book for its comprehensive approach and meticulous attention to detail. It offers a concrete explanation and an extensive bibliography that will help clarify motivations and support the development of effective solutions. Featuring over 450 carefully selected papers and books, it is an invaluable resource for anyone working on the optimal stopping problem, stochastic optimization with sequential procedures, and more. The content spans multiple stopping models, stopping games, financial applications, and numerical asymptotic solutions, providing readers with the insights they need to identify the most suitable subjects for their work. Don't miss the opportunity to add this essential title to your collection."
- Masami Yasuda, the emeritus professor at Chiba University.
“This book offers a comprehensive exploration of the fascinating field, bridging theoretical foundations with practical examples. A valuable resource, it caters to statisticians, financial mathematicians, and stochastic control experts. I wholeheartedly encourage fellow researchers and practitioners to dive into its insights. Optimal stopping strategies, discussed within, benefit not only statisticians but also professionals in finance and banking.”
-Philippe J.S. De Brouwer, HSBC and AGH University of Krakow
“Writing a comprehensive and coherent review of a broad scientific field is always a challenge, and this is certainly true for the theory and applications of optimal stopping. From the Foreword (Introduction) and the detailed table of contents, it is evident that the authors G. Sofronov and K. Szajowski have invested significant effort into this endeavour, and their work deserves sincere commendation. The book covers a vast array of optimal stopping methods and includes numerous application examples, ensuring that even seasoned experts will find new and intriguing material. The authors' expertise and dedication are apparent, making this book an invaluable resource for researchers in optimal stopping theory and those interested in its practical applications.”
-F. Thomas Bruss, Professor emeritus and Invited Professor at the department of Mathematics, Université Libre de Bruxelles
