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In real life, as well as in economic models, individuals often make decisions in an uncertain environment. In many cases, a problem which an optimizing agent faces can be formulated or reformulated as a problem of optimal timing of a certain irreversible or partially reversible action or optimal stopping problem. In this book, the authors present an alternative approach to optimal stopping problems. The basic ideas and techniques of the approach can be explained much simpler than the standard methods in the literature on optimal stopping problems. The monograph will teach the reader to apply the technique to many problems in economics and finance, including new ones. From the technical point of view, the method can be characterized as option pricing via the Wiener-Hopf factorization.
List of contents
Discrete time - discrete space models. Finite time horizon.- Real options and American options.- Risk-neutral pricing. Finite time horizon case.- Discrete time - discrete space models. Infinite time horizon.- Random walks on ?.- Options in the binomial and trinomial models.- General random walks on ?: Option pricing.- Discrete time - continuous space models.- Random walks on ?.- Basic options in the model (7.5).- Optimal stopping for general random walks.- Continuous time - continuous space models.- Brownian motion case.- General Lévy processes.- Embedded options.- Extensions.- American options with finite time horizon.- Perpetual American and real options under Ornstein-Uhlenbeck processes.
Summary
In real life, as well as in economic models, individuals often make decisions in an uncertain environment. In many cases, a problem which an optimizing agent faces can be formulated or reformulated as a problem of optimal timing of a certain irreversible or partially reversible action or optimal stopping problem. In this book, the authors present an alternative approach to optimal stopping problems. The basic ideas and techniques of the approach can be explained much simpler than the standard methods in the literature on optimal stopping problems. The monograph will teach the reader to apply the technique to many problems in economics and finance, including new ones. From the technical point of view, the method can be characterized as option pricing via the Wiener-Hopf factorization.
Additional text
From the reviews:
"In this book an alternative approach to optimal stopping problems is presented. Its basic ideas and techniques are demonstrated on a much simpler level … . Necessary notations and results of the theory of stochastic processes are introduced in a piece meal basis when they are needed. Certainly, the reading of the book is easier for readers … . The first three parts of the book can be used as an introductory course, and the rest of the book for an advanced course." (Klaus Ehemann, Zentralblatt MATH, Vol. 1131 (9), 2008)
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From the reviews:
"In this book an alternative approach to optimal stopping problems is presented. Its basic ideas and techniques are demonstrated on a much simpler level ... . Necessary notations and results of the theory of stochastic processes are introduced in a piece meal basis when they are needed. Certainly, the reading of the book is easier for readers ... . The first three parts of the book can be used as an introductory course, and the rest of the book for an advanced course." (Klaus Ehemann, Zentralblatt MATH, Vol. 1131 (9), 2008)
