Synopses & Reviews
This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.
The present monograph, based mainly on studies of the authors and their - authors, and also on lectures given by the authors in the past few years, has the following particular aims: To present basic results (with proofs) of optimal stopping theory in both discrete and continuous time using both martingale and Mar- vian approaches; To select a seriesof concrete problems ofgeneral interest from the t- ory of probability, mathematical statistics, and mathematical ?nance that can be reformulated as problems of optimal stopping of stochastic processes and solved by reduction to free-boundary problems of real analysis (Stefan problems). The table of contents found below gives a clearer idea of the material included in the monograph. Credits and historical comments are given at the end of each chapter or section. The bibliography contains a material for further reading. Acknowledgements.TheauthorsthankL.E.Dubins, S.E.Graversen, J.L.Ped- sen and L. A. Shepp for useful discussions. The authors are grateful to T. B. To- zovafortheexcellenteditorialworkonthemonograph.Financialsupportandh- pitality from ETH, Zur ] ich (Switzerland), MaPhySto (Denmark), MIMS (Man- ester) and Thiele Centre (Aarhus) are gratefully acknowledged. The authors are also grateful to INTAS and RFBR for the support provided under their grants. The grant NSh-1758.2003.1 is gratefully acknowledged. Large portions of the text were presented in the School and Symposium on Optimal Stopping with App- cations that was held in Manchester, England from 17th to 27th January 2006."
Disclosing a fascinating connection between optimal stopping problems in probability and free-boundary problems this comprehensive book covers classic methods of solution and more recent ones. Using minimal tools and key examples the book exposes optimal stopping problems at its basic principles.
Table of Contents
Preface.- Introduction.- 1. Optimal Stopping: General Facts.- 2. Stochastic Processes: A Brief Review.- 3. Optimal Stopping and Free Boundary Problems.- 4. Methods of Solution.- 5. Optimal Stopping in Stochastic Analysis.- 6. Optimal Stopping in Mathematical Statistics.- 7. Optimal Stopping in Mathematical Finance.- 8. Optimal Stopping in Financial Engineering.- Bibliography.