文档介绍：Robert R. Reitano
INTRODUCTION TO
QUANTITATIVE
FINANCE
A MATH TOOL KIT
1 1/12/10 10:00 AM
Introduction to Quantitative Finance
Introduction to Quantitative Finance
A Math Tool Kit
Robert R. Reitano
The MIT Press
Cambridge, Massachusetts
London, England
6 2010 Massachusetts Institute of Technology
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Library of Congress Cataloging-in-Publication Data
Reitano, Robert R., 1950–
Introduction to quantitative finance : a math tool kit / Robert R. Reitano.
p. cm.
Includes index.
ISBN 978-0-262-01369-7 (hardcover : alk. paper) 1. Finance—Mathematical models. I. Title.
2010
—dc22 2009022214
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Contents
List of Figures and Tables xix
Introduction xxi
1 Mathematical Logic 1
Introduction 1
Axiomatic Theory 4
Inferences 6
Paradoxes 7
Propositional Logic 10
Truth Tables 10
Framework of a Proof 15
Methods of Proof 17
The Direct Proof 19
Proof by Contradiction 19
Proof by Induction 21
* Mathematical Logic 23
Applications to Finance 24
Exercises 27
2 Number Systems and Functions 31
Numbers: Properties and Structures 31
Introduction 31
Natural Numbers 32
Integers 37
Rational Numbers 38
Real Numbers 41
* Numbers 44
Functions 49
Applications