Financial Economics, Risk and Informatio

541 Pages·2003·19.213 MB·English

by  M Bianconi, Marcelo Bianconi

FINANCIAL
ECONOMICS
RISK AND
INFORMATION
An Introduction to Methods and Models
Marcelo Bianconi
FINANCIAL ECONOMICS,
RISK AND INFORMATION
An Introduction to Methods and Models
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FINANCIAL ECONOMICS,
RISK AND INFORMATION
An Introduction to Methods and Models
Marcelo Bianconi
Tufts University, USA
World Scientific
New Jersey • London • Singapore • Hong Kong
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: Suite 202, 1060 Main Street, River Edge, NJ 07661
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
FINANCIAL ECONOMICS, RISK AND INFORMATION
An Introduction to Methods and Models
Copyright © 2003 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN 981-238-501-0
ISBN 981-238-502-9 (pbk)
Printed by Fulsland Offset Printing (S) Pte Ltd, Singapore
To Celia and Giampaolo
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FOREWORD
A few years ago, I started a new course for economics quantitative
undergraduate and graduate students with the intent of teaching how
economists and financial economists apply statistical and stochastic
methods to economic decision-making. My interest grew out of the
apparent lack of a unified course that focuses on risk and information
applied to economics and finance. This book is the result of teaching and
doing research in those areas in the last few years.
In working on this enterprise, I have benefited from several
colleagues who shared their thoughts and research with me over the
years and several students who have taken the courses I teach. In
particular, I thank Stephen Turnovsky for the fruitful collaborations,
discussions and guidance over the last several years; Yannis Ioannides
for thoughtful comments on the early stages of this project; and all my
colleagues at Tufts University who keep providing a lively and
productive intellectual environment. I thank Jun-Ho Bae, Paul Nmeke,
Benjamin Tarlow, John Tilney and all students from Tufts University
and other schools in the Boston area who made comments; and Dali Jing
and Jamie Maldonado who helped in typing some parts of the manuscript
at early stages. At World Scientific Publishing Co., I am most grateful
for the incentive and comments of the editor Yubing Zhai and the
referees she has provided; and the superb editorial execution and
assistance of Juliet Lee Ley Chin.
M. Bianconi
April 2003
Tufts University
Medford, MA
vu
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CONTENTS
Introduction 1
1. Basic Mathematical Tools
1.1 Introduction 6
1.2 Integration 6
1.3 Basic Statistics 10
1.4 Basic Linear Algebra 17
1.5 Static Optimization 20
1.6 Notes on Stochastic Difference Equations 29
1.7 Dynamic Optimization in Discrete Time: Heuristics of Dynamic
Programming in the Certainty Case 33
1.8 Stochastic Dynamic Optimization in Discrete Time 41
1.9 Notes on Stochastic Differential Equations 48
1.10 Stochastic Dynamic Optimization in Continuous Time 49
1.11 Summary 56
Problems 57
Notes on the Literature 61
References 64
2. Mean-Variance Approach to Financial
Decision-Making
2.1 Introduction 67
2.2 Portfolio Mean Return and Variance 68
2.3 The Efficient Frontier 76
2.4 Two-Fund Theorem, the Risk-Free Asset and One-Fund Theorem 82
IX