Indifference Pricing

Rene Carmona is the Paul M. Wythes '55 Professor of Engineering and Finance in the Department of Operations Research and Financial Engineering at Princeton University. His books include "Interest Rate Models and Statistical Analysis of Financial Data in S-Plus".

• 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

"This book sets out to elucidate various conceptual and methodological aspects of indifference pricing, and it succeeds with flying colors. Indifference Pricing gives an interesting overview of this new field and is written in a careful, professional, and clear manner. It will be of interest to graduate student's in mathematics, finance, and economics, as well as mathematicians working in mathematical finance and quantitatively minded economists."—Gordan Zitkovic, University of Texas, Austin