Probability via Expectation

by Whittle, Peter

• ISBN13: 9780387989556
• ISBN10: 0387989552
• Edition: 4th
• Format: Hardcover
• Copyright: 2000-03-01
• Publisher: Springer Verlag

Summary

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

Table of Contents

Preface to the Fourth Edition

Preface to the Third Edition

Preface to the Russian Edition of Probability (1982)

Preface to Probability (1970)

Uncertainty, Intuition, and Expectation

Expectation

Probability

Some Basic Models

Conditioning

Applications of the Independence Concept

The Two Basic Limit Theorems

Continuous Random Variables and Their Transformations

Markov Processes in Discrete Time

Markov Processes in Continuous Time

Action Optimisation; Dynamic Programming

Optimal Resource Allocation

Finance: 'Risk-Free' Trading and Option Pricing

Second-Order Theory

Consistency and Extension: The Finite-Dimensional Case

Stochastic Convergence

Martingales

Large-Deviation Theory

Extension: Examples of the Infinite-Dimensional Case

Quantum Mechanics

References

Index

Table of Contents provided by Blackwell. All Rights Reserved.