Indifference Pricing Theory and Applications 1st Edition by René Carmona 1400833116 9781400833115

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ISBN 10: 1400833116 

ISBN 13: 9781400833115

Author: René Carmona

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. 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

Table of contents:

PART 1. FOUNDATIONS
Chapter 1. The Single Period Binomial Model
1.1 Introduction
1.2 The Incomplete Model

Chapter 2. Utility Indifference Pricing: An Overview
2.1 Introduction
2.2 Utility Functions
2.3 Utility Indifference Prices: Definitions
2.4 Discrete Time Approach to Utility Indifference Pricing
2.5 Utility Indifference Pricing in Continuous Time
2.6 Applications, Extensions, and a Literature Review
2.7 Related Approaches
2.8 Conclusion

PART 2. DIFFUSION MODELS
Chapter 3. Pricing, Hedging, and Designing Derivatives with Risk Measures
3.1 Indifference Pricing, Capital Requirement, and Convex Risk Measures
3.2 Dilatation of Convex Risk Measures, Subdifferential and Conservative Price
3.3 Inf-Convolution
3.4 Optimal Derivative Design
3.5 Recalls on Backward Stochastic Differential Equations
3.6 Axiomatic Approach and g-Conditional Risk Measures
3.7 Dual Representation of g-Conditional Risk Measures
3.8 Inf-Convolution of g-Conditional Risk Measures
3.9 Appendix: Some Results in Convex Analysis

Chapter 4. From Markovian to Partially Observable Models
4.1 A First Diffusion Model
4.2 Static Hedging with Liquid Options
4.3 Non-Markovian Models with Full Observation
4.4 Optimal Hedging in Partially Observed Markets
4.5 The Conditionally Gaussian Case

PART 3. APPLICATIONS
Chapter 5. Portfolio Optimization
5.1 Introduction
5.2 Indifference Pricing and the Dual Formulation
5.3 Utility Indifference Pricing
5.4 Stochastic Volatility Models

Chapter 6. Indifference Pricing of Defaultable Claims
6.1 Preliminaries
6.2 Indifference Prices Relative to the Reference Filtration
6.3 Optimization Problems and BSDEs
6.4 Quadratic Hedging

Chapter 7. Applications to Weather Derivatives and Energy Contracts
7.1 Application I: Temperature Options
7.2 Application II: Rainfall Options
7.3 Application III: Commodity Derivatives

PART 4. COMPLEMENTS
Chapter 8. BSDEs and Applications
8.1 General Results on Backward Stochastic Differential Equations
8.2 Applications to Optimization Problems
8.3 Markovian BSDEs
8.4 BSDEs with Quadratic Growth with Respect to Z
8.5 Reflected Backward Stochastic Differential Equations

Chapter 9. Duality Methods
9.1 Introduction
9.2 Model
9.3 Utility Functions
9.4 Pricing Claims
9.5 The Dual Cost Function

9.6 The Minimum of Vsub(G) and Vsub(0)

9.7 The Calculation of Vsub(0)

9.8 The Indifference Asking Price for Claims

9.9 The Indifference Bid Price

9.10 Examples

9.11 Properties of υ

9.12 Numerical Methods

9.13 Approximate Formulas

9.14 An Alternative Representation for Vsub(G)

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Tags: René Carmona, Indifference, Pricing, Applications, Theory