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Optimal Stopping and Free-Boundary Problems [electronic resource] /by Goran Peskir, Albert Shiryaev.

by Peskir, Goran [author.]; Shiryaev, Albert [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Lectures in Mathematics. ETH Zürich: Publisher: Basel : Birkhäuser Basel, 2006.Description: XXII, 500p. online resource.ISBN: 9783764373900.Subject(s): Mathematics | Differential equations, partial | Finance | Mathematical optimization | Distribution (Probability theory) | Mathematics | Calculus of Variations and Optimal Control; Optimization | Probability Theory and Stochastic Processes | Partial Differential Equations | Quantitative FinanceDDC classification: 515.64 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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.
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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.

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.

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