TABLE OF CONTENTS: 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 René 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 René 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 Hamadène, 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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