Indifference pricing theory and applications edited by René Carmona.

Preface ix PART 1. FOUNDATIONS 1Chapter 1. The Single Period Binomial Model Marek Musiela and Thaleia Zariphopoulou 31.1 Introduction 31.2 The Incomplete Model 5Chapter 2. Utility Indifference Pricing: An Overview by Vicky Henderson and David Hobson 442.1 Introduction 442.2 Utility Functions 452.3 Utility Indifference Prices: Definitions 482.4 Discrete Time Approach to Utility Indifference Pricing 512.5 Utility Indifference Pricing in Continuous Time 522.6 Applications, Extensions, and a Literature Review 652.7 Related Approaches 682.8 Conclusion 72PART 2. DIFFUSION MODELS 75Chapter 3. Pricing, Hedging, and Designing Derivatives with Risk Measures by Pauline Barrieu and Nicole El Karoui 773.1 Indifference Pricing, Capital Requirement, and Convex Risk Measures 783.2 Dilatation of Convex Risk Measures, Subdifferential and Conservative Price 933.3 Inf-Convolution 983.4 Optimal Derivative Design 1053.5 Recalls on Backward Stochastic Differential Equations 1183.6 Axiomatic Approach and g-Conditional Risk Measures 1203.7 Dual Representation of g-Conditional Risk Measures 1283.8 Inf-Convolution of g-Conditional Risk Measures 1363.9 Appendix: Some Results in Convex Analysis 141Chapter 4. From Markovian to Partially Observable Models by Rene Carmona 1474.1 A First Diffusion Model 1474.2 Static Hedging with Liquid Options 1544.3 Non-Markovian Models with Full Observation 1594.4 Optimal Hedging in Partially Observed Markets 1694.5 The Conditionally Gaussian Case 174PART 3. APPLICATIONS 181Chapter 5. Portfolio Optimization by Aytac Ilhan, Mattias Jonsson, and Ronnie Sircar 1835.1 Introduction 1835.2 Indifference Pricing and the Dual Formulation 1865.3 Utility Indifference Pricing 1905.4 Stochastic Volatility Models 197Chapter 6. Indifference Pricing of Defaultable Claims by Tomasz R. Bielecki and Monique Jeanblanc 2116.1 Preliminaries 2116.2 Indifference Prices Relative to the Reference Filtration 2166.3 Optimization Problems and BSDEs 2226.4 Quadratic Hedging 230Chapter 7. Applications to Weather Derivatives and Energy Contracts by Rene Carmona 2417.1 Application I: Temperature Options 2417.2 Application II: Rainfall Options 2497.3 Application III: Commodity Derivatives 256PART 4. COMPLEMENTS 265Chapter 8. BSDEs and Applications by Nicole El Karoui, Said Hamadene, and Anis Matoussi 2678.1 General Results on Backward Stochastic Differential Equations 2698.2 Applications to Optimization Problems 2798.3 Markovian BSDEs 2858.4 BSDEs with Quadratic Growth with Respect to Z 2968.5 Reflected Backward Stochastic Differential Equations 303Chapter 9. Duality Methods by Robert J. Elliott and John van der Hoek 3219.1 Introduction 3219.2 Model 3229.3 Utility Functions 3259.4 Pricing Claims 3269.5 The Dual Cost Function 3339.6 The Minimum of VG(y) and V0(y) 3419.7 The Calculation of V0(x) 3469.8 The Indifference Asking Price for Claims 3489.9 The Indifference Bid Price 3559.10 Examples 3569.11 Properties of ? 3619.12 Numerical Methods 3649.13 Approximate Formulas 3749.14 An Alternative Representation for VG(x) 381Bibliography 387List of Contributors 405Notation Index 409Author Index 410Subject Index 413

This is the first book about the emerging field of utility indifference pricing for valuing derivatives in incomplete markets. René 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.

Includes bibliographical references and indexes.