Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach

741 Pages·2014·25.77 MB·English

by  Guojun Gan

MEASURE, PROBABILITY,
AND MATHEMATICAL
FINANCE

MEASURE, PROBABILITY,
AND MATHEMATICAL
FINANCE
A Problem-Oriented Approach
Guojun Gan
Manulife Financial
Toronto, ON, Canada
Chaoqun Ma
School of Business Administration
Hunan University
Changsha, Hunan, P.R. China
HongXie
Manulife Financial
Toronto, ON, Canada
WILEY
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Library of Congress Cataloging-in-Publication Data is available.
Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach
Guojun Gan, Chaoqun Ma, and Hong Xie
ISBN 978-1-118-83196-0
Printed in the United States of America.
10 9 8 7 6 5 4 3 2 I
To my parents
-Guojun Gan
To my wife and my
daughter
-ChaoqunMa
To my family and
friends
-Hong Xie

CONTENTS
Preface XVll
Financial Glossary xxii
PART I MEASURE THEORY
1 Sets and Sequences 3
1.1 Basic Concepts and Facts 3
1.2 Problems 6
1.3 Hints 8
1.4 Solutions 8
1.5 Bibliographic Notes 13
2 Measures 15
2.1 Basic Concepts and Facts 15
2.2 Problems 18
2.3 Hints 20
2.4 Solutions 21
vii
viii CONTENTS
2.5 Bibliographic Notes 28
3 Extension of Measures 29
3.1 Basic Concepts and Facts 29
3.2 Problems 30
3.3 Hints 32
3.4 Solutions 32
3.5 Bibliographic Notes 36
4 Lebesgue-Stieltjes Measures 37
4.1 Basic Concepts and Facts 37
4.2 Problems 39
4.3 Hints 41
4.4 Solutions 41
4.5 Bibliographic Notes 45
5 Measurable Functions 47
5.1 Basic Concepts and Facts 47
5.2 Problems 48
5.3 Hints 50
5.4 Solutions 51
5.5 Bibliographic Notes 56
6 Lebesgue Integration 57
6.1 Basic Concepts and Facts 57
6.2 Problems 59
6.3 Hints 62
6.4 Solutions 64
6.5 Bibliographic Notes 76
7 The Radon-Nikodym Theorem 77
7.1 Basic Concepts and Facts 77
7.2 Problems 79
7.3 Hints 80
7.4 Solutions 80
7.5 Bibliographic Notes 83
8 LP Spaces 85