Über die Autorin bzw. den Autor

René 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.

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"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

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"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

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Indifference Pricing

PRINCETON UNIVERSITY PRESS

Contents

Preface.............................................................................................................................ixPART 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 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 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 Ren 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 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 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 Ren 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 Nicole El Karoui, Said Hamadne, 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 Robert J. Elliott and John van der Hoek.................................................................3219.1 Introduction...................................................................................................................3219.2 Model..........................................................................................................................3229.3 Utility...