Optimal Stopping and Free-Boundary Problems

Goran Peskir, Albert Shiryaev

ISBN 10: 3764324198 / ISBN 13: 9783764324193

Published by Birkhauser Verlag AG, CH, 2006

The book aims at disclosing a fascinating connection between optimal stoppingproblems in probability and free-boundary problems in analysis using minimal toolsand focusing on key examples. The general theory of optimal stopping is exposed at thelevel of basic principles in both discrete and continuous time covering martingale andMarkovian methods. Methods of solution explained range from classic ones (such aschange of time, change of space, change of measure) to more recent ones (such as localtime-space calculus and nonlinear integral equations). A detailed chapter on stochasticprocesses is included making the material more accessible to a wider cross-disciplinaryaudience. The book may be viewed as an ideal compendium for an interested readerwho wishes to master stochastic calculus via fundamental examples.Areas of application where examples are worked out in full detail include financialmathematics (American, Russian, Asian options), financial engineering (optimalprediction of the ultimate maximum), mathematical statistics (sequential testing,quickest detection), and stochastic analysis (fundamental inequalities).Large portions of the text were not exposed in abook format before. The book also suggests anumber of new avenues for research. Seller Inventory # LU-9783764324193

Synopsis:

The book aims at disclosing a fascinating connection between optimal stoppingproblems in probability and free-boundary problems in analysis using minimal toolsand focusing on key examples. The general theory of optimal stopping is exposed at thelevel of basic principles in both discrete and continuous time covering martingale andMarkovian methods. Methods of solution explained range from classic ones (such aschange of time, change of space, change of measure) to more recent ones (such as localtime-space calculus and nonlinear integral equations). A detailed chapter on stochasticprocesses is included making the material more accessible to a wider cross-disciplinaryaudience. The book may be viewed as an ideal compendium for an interested readerwho wishes to master stochastic calculus via fundamental examples.Areas of application where examples are worked out in full detail include financialmathematics (American, Russian, Asian options), financial engineering (optimalprediction of the ultimate maximum), mathematical statistics (sequential testing,quickest detection), and stochastic analysis (fundamental inequalities).Large portions of the text were not exposed in abook format before. The book also suggests anumber of new avenues for research.

Synopsis: The book aims at disclosing a fascinating connection between optimal stopping problems in probability and free-boundary problems in analysis using minimal tools and focusing on key examples. The general theory of optimal stopping is exposed at the level of basic principles in both discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from classic ones (such as change of time, change of space, change of measure) to more recent ones (such as local time-space calculus and nonlinear integral equations). A detailed chapter on stochastic processes is included making the material more accessible to a wider cross-disciplinary audience. The book may be viewed as an ideal compendium for an interested reader who wishes to master stochastic calculus via fundamental examples. Areas of application where examples are worked out in full detail include financial mathematics, financial engineering, mathematical statistics, and stochastic analysis.

Bibliographic Details

Title: Optimal Stopping and Free-Boundary Problems
Publisher: Birkhauser Verlag AG, CH
Publication Date: 2006
Binding: Hardback
Condition: New
Edition: 2006 ed.