Stochastic Modeling In Economics And Finance

Stochastic Modeling in Economics and Finance Applied Optimization Volume 75 Series Editors: Panos M. Pardalos University of Florida, U.S.A. Donald Hearn University of Florida, U.S.A. Stochastic Modeling in Economics and Finance by Jan Hurt and Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Prague KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: Print ISBN: 0-306-48167-7 1-4020-0840-6 ©2003 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2002 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: and Kluwer's eBookstore at: http://kluweronline.com http://ebooks.kluweronline.com To my husband Václav To Jarmila, Eva, and in memory of my parents Jan Hurt To my wife Iva v CONTENTS Preface Acknowledgments xi xiii Part I Fundamentals I.1 Money, Capital, and Securities 1.1 Money and Capital 1.2 Investment 1.3 Interest 1.4 Cash Flows 1.5 Financial and Real Investment 1.6 Securities 1.7 Financial Market 1.8 Financial Institutions 1.9 Financial System I.2 Interest Rate 2.1 Simple and Compound Interest 2.2 Calendar Conventions 2.3 Determinants of the Interest Rate 2.4 Decomposition of the Interest Rate 2.5 Term Structure of Interest Rates 2.6 Continuous Compounding I.3 Measures of Cash Flows 3.1 Present Value 3.2 Annuities 3.3 Future Value 3.4 Internal Rate of Return 3.5 Duration 3.6 Convexity 3.7 Comparison of Investment Projects 3.8 Yield Curves I.4 Return, Expected Return, and Risk 4.1 Return 4.2 Risk Measurement I.5 Valuation of Securities 5.1 Coupon Bonds 5.2 Options 5.3 Forwards and Futures I.6 Matching of Assets and Liabilities 6.1 Matching and Immunization 6.2 Dedicated Bond Portfolio 6.3 A Stochastic Model of Matching I.7 Index Numbers and Inflation 7.1 Construction of Index Numbers 7.2 Stock Exchange Indicators 7.3 Inflation vii 1 1 1 1 2 2 3 12 12 12 13 13 14 15 16 18 19 21 21 23 24 26 29 30 31 36 39 39 43 48 48 52 63 64 64 65 67 68 68 70 71 I.8 Basics of Utility Theory 8.1 The Concept of Utility 8.2 Utility Function 8.3 Characteristics of Utility Functions 8.4 Some Particular Utility Functions 8.5 Risk Considerations 8.6 Certainty Equivalent I.9 Markowitz Mean-Variance Portfolio 9.1 Portfolio 9.2 Construction of Optimal Portfolios and Separation Theorems I.10 Capital Asset Pricing Model 10.1 Sharpe-Lintner Model 10.2 Security Market Line 10.3 Capital Market Line I.11 Arbitrage Pricing Theory 11.1 Regression Model 11.2 Factor Model I.12 Bibliographical Notes 73 73 73 74 75 76 77 79 80 81 92 92 93 95 96 96 97 101 Part II Discrete Time Stochastic Decision Models II.1 Introduction and Preliminaries 1.1 Problem of a Private Investor 1.2 Stochastic Dedicated Bond Portfolio 1.3 Mathematical Programs II.2 Multistage Stochastic Programs 2.1 Basic Formulations 2.2 Scenario-Based Stochastic Linear Programs 2.3 Horizon and Stages 2.4 The Flower-Girl Problem 2.5 Comparison with Stochastic Dynamic Programming II.3 Multiple Criteria 3.1 Theory 3.2 Selected Applications to Portfolio Optimization 3.3 Multi-Objective Optimization and Stochastic Programming Models II.4 Selected Applications in Finance and Economics 4.1 Portfolio Revision 4.2 The BONDS Model 4.3 Ban