Optimal Stopping and Free-Boundary Problems PDF

by Goran Peskir, Albert Shiryaev

Part of the Lectures in Mathematics. ETH Zurich series

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Description

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.