Indifference pricing : theory and applications
著者
書誌事項
Indifference pricing : theory and applications
（Princeton series in financial engineering）
Princeton University Press, c2009
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
This is the first book about the emerging field of utility indifference pricing for valuing derivatives in incomplete markets. Rene Carmona brings together a who's who of leading experts in the field to provide the definitive introduction for students, scholars, and researchers. Until recently, financial mathematicians and engineers developed pricing and hedging procedures that assumed complete markets. But markets are generally incomplete, and it may be impossible to hedge against all sources of randomness. Indifference Pricing offers cutting-edge procedures developed under more realistic market assumptions. The book begins by introducing the concept of indifference pricing in the simplest possible models of discrete time and finite state spaces where duality theory can be exploited readily. It moves into a more technical discussion of utility indifference pricing for diffusion models, and then addresses problems of optimal design of derivatives by extending the indifference pricing paradigm beyond the realm of utility functions into the realm of dynamic risk measures.
Focus then turns to the applications, including portfolio optimization, the pricing of defaultable securities, and weather and commodity derivatives. The book features original mathematical results and an extensive bibliography and indexes. In addition to the editor, the contributors are Pauline Barrieu, Tomasz R. Bielecki, Nicole El Karoui, Robert J. Elliott, Said Hamadene, Vicky Henderson, David Hobson, Aytac Ilhan, Monique Jeanblanc, Mattias Jonsson, Anis Matoussi, Marek Musiela, Ronnie Sircar, John van der Hoek, and Thaleia Zariphopoulou. * The first book on utility indifference pricing * Explains the fundamentals of indifference pricing, from simple models to the most technical ones * Goes beyond utility functions to analyze optimal risk transfer and the theory of dynamic risk measures * Covers non-Markovian and partially observed models and applications to portfolio optimization, defaultable securities, static and quadratic hedging, weather derivatives, and commodities * Includes extensive bibliography and indexes * Provides essential reading for PhD students, researchers, and professionals
目次
Preface ix PART 1. FOUNDATIONS 1 Chapter 1. The Single Period Binomial Model Marek Musiela and Thaleia Zariphopoulou 3 1.1 Introduction 3 1.2 The Incomplete Model 5 Chapter 2. Utility Indifference Pricing: An Overview by Vicky Henderson and David Hobson 44 2.1 Introduction 44 2.2 Utility Functions 45 2.3 Utility Indifference Prices: Definitions 48 2.4 Discrete Time Approach to Utility Indifference Pricing 51 2.5 Utility Indifference Pricing in Continuous Time 52 2.6 Applications, Extensions, and a Literature Review 65 2.7 Related Approaches 68 2.8 Conclusion 72 PART 2. DIFFUSION MODELS 75 Chapter 3. Pricing, Hedging, and Designing Derivatives with Risk Measures by Pauline Barrieu and Nicole El Karoui 77 3.1 Indifference Pricing, Capital Requirement, and Convex Risk Measures 78 3.2 Dilatation of Convex Risk Measures, Subdifferential and Conservative Price 93 3.3 Inf-Convolution 98 3.4 Optimal Derivative Design 105 3.5 Recalls on Backward Stochastic Differential Equations 118 3.6 Axiomatic Approach and g-Conditional Risk Measures 120 3.7 Dual Representation of g-Conditional Risk Measures 128 3.8 Inf-Convolution of g-Conditional Risk Measures 136 3.9 Appendix: Some Results in Convex Analysis 141 Chapter 4. From Markovian to Partially Observable Models by Rene Carmona 147 4.1 A First Diffusion Model 147 4.2 Static Hedging with Liquid Options 154 4.3 Non-Markovian Models with Full Observation 159 4.4 Optimal Hedging in Partially Observed Markets 169 4.5 The Conditionally Gaussian Case 174 PART 3. APPLICATIONS 181 Chapter 5. Portfolio Optimization by Aytac Ilhan, Mattias Jonsson, and Ronnie Sircar 183 5.1 Introduction 183 5.2 Indifference Pricing and the Dual Formulation 186 5.3 Utility Indifference Pricing 190 5.4 Stochastic Volatility Models 197 Chapter 6. Indifference Pricing of Defaultable Claims by Tomasz R. Bielecki and Monique Jeanblanc 211 6.1 Preliminaries 211 6.2 Indifference Prices Relative to the Reference Filtration 216 6.3 Optimization Problems and BSDEs 222 6.4 Quadratic Hedging 230 Chapter 7. Applications to Weather Derivatives and Energy Contracts by Rene Carmona 241 7.1 Application I: Temperature Options 241 7.2 Application II: Rainfall Options 249 7.3 Application III: Commodity Derivatives 256 PART 4. COMPLEMENTS 265 Chapter 8. BSDEs and Applications by Nicole El Karoui, Said Hamadene, and Anis Matoussi 267 8.1 General Results on Backward Stochastic Differential Equations 269 8.2 Applications to Optimization Problems 279 8.3 Markovian BSDEs 285 8.4 BSDEs with Quadratic Growth with Respect to Z 296 8.5 Reflected Backward Stochastic Differential Equations 303 Chapter 9. Duality Methods by Robert J. Elliott and John van der Hoek 321 9.1 Introduction 321 9.2 Model 322 9.3 Utility Functions 325 9.4 Pricing Claims 326 9.5 The Dual Cost Function 333 9.6 The Minimum of VG(y) and V0(y) 341 9.7 The Calculation of V0(x) 346 9.8 The Indifference Asking Price for Claims 348 9.9 The Indifference Bid Price 355 9.10 Examples 356 9.11 Properties of ? 361 9.12 Numerical Methods 364 9.13 Approximate Formulas 374 9.14 An Alternative Representation for VG(x) 381 Bibliography 387 List of Contributors 405 Notation Index 409 Author Index 410 Subject Index 413
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