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Optimal Stopping and Free-Boundary Problems

  • Goran Peskir
  • Albert Shiryaev

Part of the Lectures in Mathematics. ETH Zürich book series (LM)

Table of contents

About this book

Introduction

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.

Keywords

Analysis Financial mathematics Mathematical statistics Measure Stochastic Processes Stochastic analysis Stochastic process stochastic calculus

Authors and affiliations

  • Goran Peskir
    • 1
  • Albert Shiryaev
    • 2
    • 3
  1. 1.School of MathematicsThe University of ManchesterManchesterUK
  2. 2.Steklov Mathematical InstituteMoscowRussia
  3. 3.GSP-2 Leninskie GoryMoscow State UniversityMoscowRussia

Bibliographic information