发帖
雷达卡
0691138834.pdf
(2.11 MB, 需要: 5 个论坛币)
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 Hamadène, 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
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.
Endorsement:
"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
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
京公网安备 11010802022788号
