Details
Optimal Stopping and Free-Boundary Problems
Lectures in Mathematics. ETH Zürich
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139,09 € |
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| Verlag: | Birkhäuser |
| Format: | |
| Veröffentl.: | 10.11.2006 |
| ISBN/EAN: | 9783764373900 |
| Sprache: | englisch |
| Anzahl Seiten: | 522 |
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Beschreibungen
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.
Optimal stopping: General facts.- Stochastic processes: A brief review.- Optimal stopping and free-boundary problems.- Methods of solution.- Optimal stopping in stochastic analysis.- Optimal stopping in mathematical statistics.- Optimal stopping in mathematical finance.- Optimal stopping in financial engineering.
A comprehensive treatment of optimal stopping and free-boundary problems ranging from pure theoretical aspects describing methods of solution to specific examples worked out in full detail Marries the three classic problem formulations due to Lagrange (18th century), Mayer (19th century) and Bolza (1913) with the modern problem formulation based on the maximum functional to produce a unifying theory Deals with the principles of smooth and continuous fit in a unifying way Presents complete solutions to option problems (American, Russian, Asian) using local time-space calculus and nonlinear integral equations Presents solutions to problems of optimal prediction of the ultimate maximum opening new avenues for research Includes supplementary material: sn.pub/extras
<P>A fascinating connection between optimal stopping and free-boundary problems are covered by this book. The analysis uses minimal tools and focuses on key examples. The general theory of optimal stopping is exposed at its basic principles in both discrete and continuous time. It marries the classic methods of solution with more recent ones and a detailed chapter on stochastic processes makes the material more accessible to a wider cross-disciplinary audience. The book is an ideal compendium for an interested reader wishing to master stochastic calculus via fundamental examples. Areas of application where examples are worked out in full detail include financial mathematics, financial engineering, and mathematical statistics. The book will appeal to graduate and postgraduate students, researchers, and practitioners.</P>
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