Probability via Expectation (Springer Texts in Statistics) - Hardcover

Whittle, Peter

Hardcover

ISBN 10: 0387989552 ISBN 13: 9780387989556

Publisher: Springer, 2000

Synopsis

This book has exerted a continuing appeal since its original publication in 1970. It develops the theory of probability from axioms on the expectation functional rather than on probability measure, demonstrates that the standard theory unrolls more naturally and economically this way, and that applications of real interest can be addressed almost immediately. A secondary aim of the original text was to introduce fresh examples and convincing applications, and that aim is continued in this edition, a general revision plus the addition of chapters giving an economical introduction to dynamic programming, that is then applied to the allocation problems represented by portfolio selection and the multi-armed bandit. The investment theme is continued with a critical investigation of the concept of risk-free'trading and the associated Black-Sholes formula, while another new chapter develops the basic ideas of large deviations. The book may be seen as an introduction to probability for students with a basic mathematical facility, covering the standard material, but different in that it is unified by its theme and covers an unusual range of modern applications.

About this title

Review

From the reviews of the fourth edition:

"... a clear success in its unorthodoxy, Probability via Expectation has become a treasured classic."
P.A.L. Emrechts in "Short Book Reviews", Vol. 21/1, April, 2001

"Apart from presenting a case for the development of probability theory by using the expectation operator rather than probability measure as the primitive notion, a second distinctive feature of this book is the very large range of modern applications that it covers. Many of these are addressed by more than 350 exercises interspersed throughout the text. In summary, this well written book is a ... introduction to probability theory and its applications." (Norbert Henze, Metrika, November, 2002)

"Originally published in 1970, this book has stood the test of time. ... the text demonstrates a modern alternative approach to a now classical field. ... The fourth edition contains a number of modifications and corrections. New material on dynamic programming, optimal allocation, options pricing and large deviations is included." (Martin T. Wells, Journal of the American Statistical Association, September 2001)

Synopsis

This book has exerted a continuing appeal since publication of its original edition in 1970. It develops the theory of probability from axioms on the expectation functional rather than on probability measure, demonstrates that the standard theory unrolls more naturally and economically this way, and demonstrates that applications of real interest can be addressed almost immediately. Early analysts of games of chance found the question 'What is the fair price for entering this game?' quite as natural as 'What is the probability of winning it?' Modern probability virtually adopts the former view; present-day treatments of conditioning, weak convergence, generalised processes and, notably, quantum mechanics start explicitly from an expectation characterisation. A secondary aim of the original text was to introduce fresh examples and convincing applications, and that aim is continued in this edition, a general revision plus addition of Chapters 11, 12, 13, and 18.Chapter 11 gives an economical introduction to dynamic programming, applied in Chapter 12 to the allocation problems represented by portfolio selection and the multi-armed bandit.

The investment theme is continued in Chapter 13 with a critical investigation of the concept of 'risk-free' trading and the associated Black-Sholes formula. Chapter 18 develops the basic ideas of large deviations, now a standard and invaluable component of theory and tool in applications. The book is seen as an introduction to probability for students with a basic mathematical facility, covering the standard material, but different in that it is unified by its theme and covers an unusual range of modern applications. For these latter reasons it is of interest to a wide class of readers; probabilists will find the alternative approach of interest, physicists ad engineers will find it.

Edition details

• Publisher: Springer
• Publication date: 2000
• ISBN 10: 0387989552
• ISBN 13: 9780387989556
• Binding: Hardcover
• Language: English
• Edition number: 4
• Number of pages: 374