Stochastic Modeling in Economics and Finance

Stochastic Modeling in Economics and Finance

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English

Description

Unlike other books that focus only on selected specific subjects this book provides both a broad and rich cross-section of contemporary approaches to stochastic modeling in finance and economics; it is decision making oriented. The material ranges from common tools to solutions of sophisticated system problems and applications.
In Part I, the fundamentals of financial thinking and elementary mathematical methods of finance are presented. The method of presentation is simple enough to bridge the elements of financial arithmetic and complex models of financial math developed in the later parts. It covers characteristics of cash flows, yield curves, and valuation of securities.
Part II is devoted to the allocation of funds and risk management: classics (Markowitz theory of portfolio), capital asset pricing model, arbitrage pricing theory, asset & liability management, value at risk. The method explanation takes into account the computational aspects.
Part III explains modeling aspects of multistage stochastic programming on a relatively accessible level. It includes a survey of existing software, links to parametric, multiobjective and dynamic programming, and to probability and statistics. It focuses on scenario-based problems with the problems of scenario generation and output analysis discussed in detail and illustrated within a case study. Selected examples of successful applications in finance, production planning and management of technological processes and electricity generation are presented. Throughout, the emphasis is on the appropriate use of the techniques, rather than on the underlying mathematical proofs and theories.
In Part IV, the sections devoted to stochastic calculus cover also more advanced topics such as DDS Theorem or extremal martingale measures, which make it possible to treat more delicate models in Mathematical Finance (complete markets, optimal control, etc.)
Audience: Students and researchers in probability and statistics, econometrics, operations research and various fields of finance, economics, engineering, and insurance.

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Published by
Published 01 January 1983
Reads 12
EAN13 0306481677
License: All rights reserved
Language English

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CONTENTS
Preface Acknowledgments
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
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xi xiii
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
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 Bank Asset and Liability Management – Model ALM 4.4 General Features of Multiperiod Stochastic Programs in Finance 4.5 Production Planning 4.6 Capacity Expansion of Electric Power Generation Systems – CEP 4.7 Unit Commitment and Economic Power Dispatch Problem 4.8 Melt Control: Charge Optimization II.5 Approximation Via Scenarios 5.1 Introduction 5.2 Scenarios and their Generation 5.3 How to Draw Inference about the True Problem
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73 73 73 74 75 76 77 79 80 81 92 92 93 95 96 96 97 101
103 104 105 106 108 108 112 115 117 119 123 123 127 131 137 137 139 141 144 148 150 153 154 158 158 159 164
5.4 Scenario Trees for Multistage Stochastic Programs II.6 Case Study: Bond Portfolio Management Problem 6.1 The Problem and the Input Data 6.2 The Model and the Structure of the Program 6.3 Generation of Scenarios 6.4 Selected Numerical Results 6.5 “What if” Analysis 6.6 Discussion II.7 Incomplete Input Information 7.1 Sensitivity for the BlackScholes Formula 7.2 Markowitz MeanVariance Model 7.3 Incomplete Information about Liabilities II.8 Numerical Techniques and Available Software (by Pavel Popela) 8.1 Motivation 8.2 Common Optimization Techniques 8.3 Solution Techniques for TwoStage Stochastic Programs 8.4 Solution Techniques for Multistage Stochastic Programs 8.5 Approximation Techniques 8.6 Model Management II.9 Bibliographical Notes Part III Stochastic Analysis and Diffusion Finance III.1 Martingales 1.1 Stochastic Processes 1.2 Brownian Motion and Martingales 1.3 Markov Times and Stopping Theorem 1.4 Local Martingales and Complete Filtrations 1.5 and Density Theorem 1.6 DoobMeyer Decomposition 1.7 Quadratic Variation of Local Martingales 1.8 Helps to Some Exercises III.2 Stochastic Integration 2.1 Stochastic Integral 2.2 Stochastic Per Partes and Itô Formula 2.3 Exponential Martingales and Lévy Theorem 2.4 Girsanov Theorem 2.5 Integral and Brownian Representations 2.6 Helps to Some Exercises III.3 Diffusion Financial Mathematics 3.1 BlackScholes Calculus 3.2 Girsanov Calculus 3.3 Market Regulations and Option Pricing 3.4 Helps to Some Exercises III. 4 Bibliographical Notes References Index
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169 180 180 182 187 190 192 197 199 199 200 204 206 206 208 214 218 224 226 228
231 231 238 244 252 257 263 269 275 277 277 286 295 300 308 316 319 319 333 350 363 366 369 377