Stochastic modeling in economics and finance:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2002
|
| Schriftenreihe: | Applied optimization
75 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 386 S. graph. Darst. |
| ISBN: | 1402008406 |
Internformat
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| 245 | 1 | 0 | |a Stochastic modeling in economics and finance |c by Jitka Dupačová, Jan Hurt and Josef Štěpán |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 2002 | |
| 300 | |a XIII, 386 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804138258698862592 |
|---|---|
| adam_text | CONTENTS
Preface xi
Acknowledgments xiii
Part I Fundamentals
1.1 Money, Capital, and Securities 1
1.1 Money and Capital 1
1.2 Investment 1
1.3 Interest 1
1.4 Cash Flows 2
1.5 Financial and Real Investment 2
1.6 Securities 3
1.7 Financial Market 12
1.8 Financial Institutions 12
1.9 Financial System 12
1.2 Interest Rate 13
2.1 Simple and Compound Interest 13
2.2 Calendar Conventions 14
2.3 Determinants of the Interest Rate 15
2.4 Decomposition of the Interest Rate 16
2.5 Term Structure of Interest Rates 18
2.6 Continuous Compounding 19
1.3 Measures of Cash Flows 21
3.1 Present Value 21
3.2 Annuities 23
3.3 Future Value 24
3.4 Internal Rate of Return 26
3.5 Duration 29
3.6 Convexity 30
3.7 Comparison of Investment Projects 31
3.8 Yield Curves 36
1.4 Return, Expected Return, and Risk 39
4.1 Return 39
4.2 Risk Measurement 43
1.5 Valuation of Securities 48
5.1 Coupon Bonds 48
5.2 Options 52
5.3 Forwards and Futures 63
1.6 Matching of Assets and Liabilities 64
6.1 Matching and Immunization 64
6.2 Dedicated Bond Portfolio 65
6.3 A Stochastic Model of Matching 67
1.7 Index Numbers and Inflation 68
7.1 Construction of Index Numbers 68
7.2 Stock Exchange Indicators 70
7.3 Inflation 71
vii
1.8 Basics of Utility Theory 73
8.1 The Concept of Utility 73
8.2 Utility Function 73
8.3 Characteristics of Utility Functions 74
8.4 Some Particular Utility Functions 75
8.5 Risk Considerations 76
8.6 Certainty Equivalent 77
1.9 Markowitz Mean-Variance Portfolio 79
9.1 Portfolio 80
9.2 Construction of Optimal Portfolios and Separation Theorems 81
1.10 Capital Asset Pricing Model 92
10.1 Sharpe-Lintner Model 92
10.2 Security Market Line 93
10.3 Capital Market Line 95
1.11 Arbitrage Pricing Theory 96
11.1 Regression Model 96
11.2 Factor Model 97
1.12 Bibliographical Notes 101
Part II Discrete Time Stochastic Decision Models
II. 1 Introduction and Preliminaries 103
1.1 Problem of a Private Investor 104
1.2 Stochastic Dedicated Bond Portfolio 105
1.3 Mathematical Programs 106
11.2 Multistage Stochastic Programs 108
2.1 Basic Formulations 108
2.2 Scenario-Based Stochastic Linear Programs 112
2.3 Horizon and Stages 116
2.4 The Flower-Girl Problem 117
2.5 Comparison with Stochastic Dynamic Programming 119
11.3 Multiple Criteria 123
3.1 Theory 123
3.2 Selected Applications to Portfolio Optimization 127
3.3 Multi-Objective Optimization and Stochastic Programming Models 131
11.4 Selected Applications in Finance and Economics 137
4.1 Portfolio Revision 137
4.2 The BONDS Model 139
4.3 Bank Asset and Liability Management - Model ALM 141
4.4 General Features of Multiperiod Stochastic Programs in Finance 144
4.5 Production Planning 148
4.6 Capacity Expansion of Electric Power Generation Systems - CEP 150
4.7 Unit Commitment and Economic Power Dispatch Problem 153
4.8 Melt Control: Charge Optimization 154
11.5 Approximation Via Scenarios 158
5.1 Introduction 158
5.2 Scenarios and their Generation 159
5.3 How to Draw Inference about the True Problem 164
vtti
5.4 Scenario Trees for Multistage Stochastic Programs 169
II.6 Case Study: Bond Portfolio Management Problem 180
6.1 The Problem and the Input Data 180
6.2 The Model and the Structure of the Program 182
6.3 Generation of Scenarios 187
6.4 Selected Numerical Results 190
6.5 What if Analysis 192
6.6 Discussion 197
II. 7 Incomplete Input Information 199
7.1 Sensitivity for the Black-Scholes Formula 199
7.2 Markowitz Mean-Variance Model 200
7.3 Incomplete Information about Liabilities 204
11.8 Numerical Techniques and Available Software (by Pavel Popela) 206
8.1 Motivation 206
8.2 Common Optimization Techniques 208
8.3 Solution Techniques for Two-Stage Stochastic Programs 214
8.4 Solution Techniques for Multistage Stochastic Programs 218
8.5 Approximation Techniques 224
8.6 Model Management 226
11.9 Bibliographical Notes 228
Part III Stochastic Analysis and Diffusion Finance
111.1 Martingales 231
1.1 Stochastic Processes 231
1.2 Brownian Motion and Martingales 238
1.3 Markov Times and Stopping Theorem 244
1.4 Local Martingales and Complete Filtrations 252
1.5 Z^-Martingales and Density Theorem 257
1.6 Doob-Meyer Decomposition 263
1.7 Quadratic Variation of Local Martingales 269
1.8 Helps to Some Exercises 275
111.2 Stochastic Integration 277
2.1 Stochastic Integral 277
2.2 Stochastic Per Partes and Ito Formula 286
2.3 Exponential Martingales and Levy Theorem 295
2.4 Girsanov Theorem 300
2.5 Integral and Brownian Representations 308
2.6 Helps to Some Exercises 316
111.3 Diffusion Financial Mathematics 319
3.1 Black-Scholes Calculus 319
3.2 Girsanov Calculus 333
3.3 Market Regulations and Option Pricing 350
3.4 Helps to Some Exercises 363
III. 4 Bibliographical Notes 366
References 369
Index 377
ix
|
| adam_txt |
CONTENTS
Preface xi
Acknowledgments xiii
Part I Fundamentals
1.1 Money, Capital, and Securities 1
1.1 Money and Capital 1
1.2 Investment 1
1.3 Interest 1
1.4 Cash Flows 2
1.5 Financial and Real Investment 2
1.6 Securities 3
1.7 Financial Market 12
1.8 Financial Institutions 12
1.9 Financial System 12
1.2 Interest Rate 13
2.1 Simple and Compound Interest 13
2.2 Calendar Conventions 14
2.3 Determinants of the Interest Rate 15
2.4 Decomposition of the Interest Rate 16
2.5 Term Structure of Interest Rates 18
2.6 Continuous Compounding 19
1.3 Measures of Cash Flows 21
3.1 Present Value 21
3.2 Annuities 23
3.3 Future Value 24
3.4 Internal Rate of Return 26
3.5 Duration 29
3.6 Convexity 30
3.7 Comparison of Investment Projects 31
3.8 Yield Curves 36
1.4 Return, Expected Return, and Risk 39
4.1 Return 39
4.2 Risk Measurement 43
1.5 Valuation of Securities 48
5.1 Coupon Bonds 48
5.2 Options 52
5.3 Forwards and Futures 63
1.6 Matching of Assets and Liabilities 64
6.1 Matching and Immunization 64
6.2 Dedicated Bond Portfolio 65
6.3 A Stochastic Model of Matching 67
1.7 Index Numbers and Inflation 68
7.1 Construction of Index Numbers 68
7.2 Stock Exchange Indicators 70
7.3 Inflation 71
vii
1.8 Basics of Utility Theory 73
8.1 The Concept of Utility 73
8.2 Utility Function 73
8.3 Characteristics of Utility Functions 74
8.4 Some Particular Utility Functions 75
8.5 Risk Considerations 76
8.6 Certainty Equivalent 77
1.9 Markowitz Mean-Variance Portfolio 79
9.1 Portfolio 80
9.2 Construction of Optimal Portfolios and Separation Theorems 81
1.10 Capital Asset Pricing Model 92
10.1 Sharpe-Lintner Model 92
10.2 Security Market Line 93
10.3 Capital Market Line 95
1.11 Arbitrage Pricing Theory 96
11.1 Regression Model 96
11.2 Factor Model 97
1.12 Bibliographical Notes 101
Part II Discrete Time Stochastic Decision Models
II. 1 Introduction and Preliminaries 103
1.1 Problem of a Private Investor 104
1.2 Stochastic Dedicated Bond Portfolio 105
1.3 Mathematical Programs 106
11.2 Multistage Stochastic Programs 108
2.1 Basic Formulations 108
2.2 Scenario-Based Stochastic Linear Programs 112
2.3 Horizon and Stages 116
2.4 The Flower-Girl Problem 117
2.5 Comparison with Stochastic Dynamic Programming 119
11.3 Multiple Criteria 123
3.1 Theory 123
3.2 Selected Applications to Portfolio Optimization 127
3.3 Multi-Objective Optimization and Stochastic Programming Models 131
11.4 Selected Applications in Finance and Economics 137
4.1 Portfolio Revision 137
4.2 The BONDS Model 139
4.3 Bank Asset and Liability Management - Model ALM 141
4.4 General Features of Multiperiod Stochastic Programs in Finance 144
4.5 Production Planning 148
4.6 Capacity Expansion of Electric Power Generation Systems - CEP 150
4.7 Unit Commitment and Economic Power Dispatch Problem 153
4.8 Melt Control: Charge Optimization 154
11.5 Approximation Via Scenarios 158
5.1 Introduction 158
5.2 Scenarios and their Generation 159
5.3 How to Draw Inference about the True Problem 164
vtti
5.4 Scenario Trees for Multistage Stochastic Programs 169
II.6 Case Study: Bond Portfolio Management Problem 180
6.1 The Problem and the Input Data 180
6.2 The Model and the Structure of the Program 182
6.3 Generation of Scenarios 187
6.4 Selected Numerical Results 190
6.5 "What if Analysis 192
6.6 Discussion 197
II. 7 Incomplete Input Information 199
7.1 Sensitivity for the Black-Scholes Formula 199
7.2 Markowitz Mean-Variance Model 200
7.3 Incomplete Information about Liabilities 204
11.8 Numerical Techniques and Available Software (by Pavel Popela) 206
8.1 Motivation 206
8.2 Common Optimization Techniques 208
8.3 Solution Techniques for Two-Stage Stochastic Programs 214
8.4 Solution Techniques for Multistage Stochastic Programs 218
8.5 Approximation Techniques 224
8.6 Model Management 226
11.9 Bibliographical Notes 228
Part III Stochastic Analysis and Diffusion Finance
111.1 Martingales 231
1.1 Stochastic Processes 231
1.2 Brownian Motion and Martingales 238
1.3 Markov Times and Stopping Theorem 244
1.4 Local Martingales and Complete Filtrations 252
1.5 Z^-Martingales and Density Theorem 257
1.6 Doob-Meyer Decomposition 263
1.7 Quadratic Variation of Local Martingales 269
1.8 Helps to Some Exercises 275
111.2 Stochastic Integration 277
2.1 Stochastic Integral 277
2.2 Stochastic Per Partes and Ito Formula 286
2.3 Exponential Martingales and Levy Theorem 295
2.4 Girsanov Theorem 300
2.5 Integral and Brownian Representations 308
2.6 Helps to Some Exercises 316
111.3 Diffusion Financial Mathematics 319
3.1 Black-Scholes Calculus 319
3.2 Girsanov Calculus 333
3.3 Market Regulations and Option Pricing 350
3.4 Helps to Some Exercises 363
III. 4 Bibliographical Notes 366
References 369
Index 377
ix |
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| id | DE-604.BV023597367 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:42:09Z |
| indexdate | 2024-07-09T21:25:20Z |
| institution | BVB |
| isbn | 1402008406 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016912499 |
| oclc_num | 610978509 |
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| owner_facet | DE-521 DE-11 |
| physical | XIII, 386 S. graph. Darst. |
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| series | Applied optimization |
| series2 | Applied optimization |
| spelling | Dupačová, Jitka Verfasser aut Stochastic modeling in economics and finance by Jitka Dupačová, Jan Hurt and Josef Štěpán Dordrecht [u.a.] Kluwer Acad. Publ. 2002 XIII, 386 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied optimization 75 Mathematisches Modell Wirtschaft Economics -- Mathematical models Finance -- Mathematical models Stochastic analysis Volkswirtschaftslehre (DE-588)4078943-3 gnd rswk-swf Finanzierung (DE-588)4017182-6 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Volkswirtschaftslehre (DE-588)4078943-3 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Finanzierung (DE-588)4017182-6 s Hurt, Jan Verfasser aut Štěpán, Josef Verfasser aut Applied optimization 75 (DE-604)BV010841718 75 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016912499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dupačová, Jitka Hurt, Jan Štěpán, Josef Stochastic modeling in economics and finance Applied optimization Mathematisches Modell Wirtschaft Economics -- Mathematical models Finance -- Mathematical models Stochastic analysis Volkswirtschaftslehre (DE-588)4078943-3 gnd Finanzierung (DE-588)4017182-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4078943-3 (DE-588)4017182-6 (DE-588)4057633-4 |
| title | Stochastic modeling in economics and finance |
| title_auth | Stochastic modeling in economics and finance |
| title_exact_search | Stochastic modeling in economics and finance |
| title_exact_search_txtP | Stochastic modeling in economics and finance |
| title_full | Stochastic modeling in economics and finance by Jitka Dupačová, Jan Hurt and Josef Štěpán |
| title_fullStr | Stochastic modeling in economics and finance by Jitka Dupačová, Jan Hurt and Josef Štěpán |
| title_full_unstemmed | Stochastic modeling in economics and finance by Jitka Dupačová, Jan Hurt and Josef Štěpán |
| title_short | Stochastic modeling in economics and finance |
| title_sort | stochastic modeling in economics and finance |
| topic | Mathematisches Modell Wirtschaft Economics -- Mathematical models Finance -- Mathematical models Stochastic analysis Volkswirtschaftslehre (DE-588)4078943-3 gnd Finanzierung (DE-588)4017182-6 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Mathematisches Modell Wirtschaft Economics -- Mathematical models Finance -- Mathematical models Stochastic analysis Volkswirtschaftslehre Finanzierung Stochastisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016912499&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010841718 |
| work_keys_str_mv | AT dupacovajitka stochasticmodelingineconomicsandfinance AT hurtjan stochasticmodelingineconomicsandfinance AT stepanjosef stochasticmodelingineconomicsandfinance |