Applied stochastic models and control for finance and insurance:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, Mass. [u.a.]
Kluwer
1998
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 341 S. graph. Darst. |
| ISBN: | 0792381483 |
Internformat
MARC
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| 100 | 1 | |a Tapiero, Charles S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied stochastic models and control for finance and insurance |c by Charles S. Tapiero |
| 264 | 1 | |a Boston, Mass. [u.a.] |b Kluwer |c 1998 | |
| 300 | |a 341 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Dynamisches Modell / Dynamische Optimierung / Stochastischer Prozess / Markovscher Prozess / Kapitalanlage / Portfolio-Management / Theorie | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Investments -- Mathematical models | |
| 650 | 4 | |a Insurance -- Mathematical models | |
| 650 | 4 | |a Stochastic processes | |
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Datensatz im Suchindex
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| adam_text | TABLE OF CONTENTS
1 : DYNAMICS, STOCHASTIC MODELS AND UNCERTAINTY 1
1.1 Introduction 1
1.2 On Dynamic Models 1
(i) Preference and Decision Flexibility 4
(ii) Time Structure of Transformation Processes 6
(Hi) Memory 6
1.3 Applications and Decision Making over Time 9
(i) Planning 9
(ii) Risk Management 10
(Hi) Information Systems 11
(iv) The Firm and Decision Making Under Uncertainty 12
(v) Insurance and Actuarial Science 14
1.4 Uncertainty and Risk in Finance 16
(i) Risks in Finance 16
(ii) Inflation 18
(Hi) Volatility estimation in finance 19
1.5 Financial Instruments 20
1.6 Options 22
(i) Valuing a Simple Option : Arbitrage and a two periods option 23
(ii) Options on Real Assets 28
1.7 Banking and Portfolio Risk 30
1.8 Decision Making, Utility and Uncertainty 31
(i) Utility and Risk Behavior 33
Further Reading 40
2 : MODELLING : MARKOV CHAINS AND MARKOV PROCESSES 41
2.1 Introduction 41
2.2 Markov Chains and Applications 42
2.3 Passage Time 52
2.4 Classification of the States of a Markov Chain 55
2.5 Markov Processes in Continuous State and Discrete Time 56
2.6 Applications 58
Mathematical Appendix 76
A. 1. Review of Basic Probability Notions 76
t
A. 2. The moments of probability distributions 77
A. 3. Order statistics 79
A. 4. Stochastic Convergence 79
A. 5. Generating Functions 80
A.6. Stationarity, Ergodicity and Independent Increments 82
A. 7. Martingales 84
A.8. Bonds, Interest rates and yield curve mathematics 85
3 : RANDOM WALKS AND STOCHASTIC DIFFERENTIAL EQUATIONS 89
3.1 Random Walks and Applications 89
3.2 The Wiener Process and Brown ian Motion 101
3.3 Stochastic Differential Equations 103
3.4 Ito s Stochastic Calculus 105
3.5 Applications 110
3.6 Applications in Finance and Insurance 119
3.7 Stochastic Differential Equations and the Fokker Planck Equation 127
3.8 Black Scholes Option Formula 129
(i) Options, their sensitivity and hedging parameters 133
(ii) Options PUT CALL Parity 134
3.9 Interest Rate Processes 135
3.10 More on Contracts, Options and Futures 139
(1) Pricing Derivative Assets : General Case 139
(2) Bond Options: Default Free and Junk Bonds 140
(3) Other Options 145
Further Reading 146
4 : JUMP PROCESSES AND SPECIAL PROBLEMS 147
4.1 Introduction 147
4.2 Jump processes 147
4.3 The Birth Death Random Walk 153
(1) The BD Model in continuous time 154
(2) The BD Model in continuous time with distributed times between jumps 154
(2) The Randomized Random Walk Distribution 156
(4) The BD Model and the Wiener Process (*) 157
4.4 Reflection and Absorption Processes 159
4.5 First Passage Time 165
4.6 Martingales and Finance* 172
(i) Martingales in Continuous Time Processes 173
(ii) Martingales, Risk Neutral Pricing and Girsanov s Theorem 175
(Hi) Girsanov s theorem and the Price of Risk 177
4.7 Other Processes 177
(i) Recurrent Events and the Renewal Equation 178
(ii) The Renewal Equation 179
(Hi) Branching Processes 180
(iv) Semi Markov Processes 180
Further Reading 182
5. MEMORY, VOLATILITY MODELS AND THE RANGE PROCESS 183
5.1 Models of Memory 183
5.2 ARCH, GARCH and Volatility Models 191
5.3 The Range Process 197
(i) The range of a random sample 198
(ii) The Variance Process 199
(Hi) The inverse range process 202
(iv) The Moments of the Inverse Range Process 207
(v) The Range Process of Wiener processes 209
(vi) The range probability distribution of a random walk 212
5.4 R/S Analysis and Applications 213
(i) R/S Analysis for a Birth Death Random Walk 214
(ii) The R/S statistic for Birth Death random walks 217
(Hi) R/S tests for volatility 221
(iv) Hurst Exponent 221
(v) Approximate Range Process Analysis and Detection 222
(vi) Process Reliability and Volatility 224
5.5 Probability Modelling, Randomness and Chaos 226
Further Reading 232
Mathematical Appendix 234
6. DYNAMIC OPTIMIZATION 237
6.1 Stochastic Dynamic Programming (SDP) 237
(1) Bellman s Equation and Dynamic Programming Til
(2) Bellman s Equation for Stochastic Dynamic Programming 242
(3) Examples and Problems 242
(5) Stochastic Dynamic Programming in Continuous Time 245
6.2 The Dynamic Programming Equations for Selected Processes 247
(1) Wiener Process 247
(2) Random Walks 254
(3) A Jump Process 255
(4) Random Planning Time 257
(6) Infinite Horizon Time 262
(7) Optimum Stopping Times 263
(8) Average Cost Criteria 264
(9) Optimization with Reflection 265
(10) Impulse Control 266
6.3 The Maximum Principle Approach 270
(I) Interpreting stochastic control problems 272
Further Reading 274
7. NUMERICAL AND OPTIMIZATION TECHNIQUES 275
7.1 Introduction 275
7.2 Approximating Stochastic Differential Equations 276
(!) Markov Chains 276
(ii) Moments approximations 281
(Hi) Approximations to stochastic differential equations by integration 283
(iv) Approximations based on the Stratonovich SDE 285
7.3 Discretization Techniques for the PDE 286
(i) Finite differencing 286
(ii) Finite Element Methods 290
7.4 Approximate Solutions to Stochastic Control Problems 290
(i) MDP Formulations of Stochastic Control Problems 291
(ii) Perturbation Techniques 293
(Hi) Monte Carlo Techniques and Stochastic Approximations 293
7.5 Expert Systems and Stochastic Dynamic Programming Software 295
7.6 Ex Post and Scenario Optimization 297
Further Reading 298
Mathematical Appendix 299
A. 1 Taylor series and Convexity 299
A.2 Introductory optimization 301
A. 3 Stochastic Programming 303
A. 4 Nonlinear programming software 305
|
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| dewey-ones | 332 - Financial economics |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV012173866 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:23:01Z |
| institution | BVB |
| isbn | 0792381483 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008248273 |
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| physical | 341 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Kluwer |
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| spelling | Tapiero, Charles S. Verfasser aut Applied stochastic models and control for finance and insurance by Charles S. Tapiero Boston, Mass. [u.a.] Kluwer 1998 341 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dynamisches Modell / Dynamische Optimierung / Stochastischer Prozess / Markovscher Prozess / Kapitalanlage / Portfolio-Management / Theorie Mathematisches Modell Investments -- Mathematical models Insurance -- Mathematical models Stochastic processes Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Operations Research (DE-588)4043586-6 s Stochastisches Modell (DE-588)4057633-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008248273&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tapiero, Charles S. Applied stochastic models and control for finance and insurance Dynamisches Modell / Dynamische Optimierung / Stochastischer Prozess / Markovscher Prozess / Kapitalanlage / Portfolio-Management / Theorie Mathematisches Modell Investments -- Mathematical models Insurance -- Mathematical models Stochastic processes Stochastisches Modell (DE-588)4057633-4 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4043586-6 |
| title | Applied stochastic models and control for finance and insurance |
| title_auth | Applied stochastic models and control for finance and insurance |
| title_exact_search | Applied stochastic models and control for finance and insurance |
| title_full | Applied stochastic models and control for finance and insurance by Charles S. Tapiero |
| title_fullStr | Applied stochastic models and control for finance and insurance by Charles S. Tapiero |
| title_full_unstemmed | Applied stochastic models and control for finance and insurance by Charles S. Tapiero |
| title_short | Applied stochastic models and control for finance and insurance |
| title_sort | applied stochastic models and control for finance and insurance |
| topic | Dynamisches Modell / Dynamische Optimierung / Stochastischer Prozess / Markovscher Prozess / Kapitalanlage / Portfolio-Management / Theorie Mathematisches Modell Investments -- Mathematical models Insurance -- Mathematical models Stochastic processes Stochastisches Modell (DE-588)4057633-4 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Dynamisches Modell / Dynamische Optimierung / Stochastischer Prozess / Markovscher Prozess / Kapitalanlage / Portfolio-Management / Theorie Mathematisches Modell Investments -- Mathematical models Insurance -- Mathematical models Stochastic processes Stochastisches Modell Operations Research |
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