This book is the first volume in a series of treatises in financial engineering to be publishedby the Princeton University Press. It would not have been possible without the encouragement of E. Cinlar and the generous financial support of W. Neidig.
It is an introduction to the subtle intricacies of utility-based pricing. It consists of the joint efforts of authors who have led the research on this field. Each chapter can be read independently of others, but the book is better than the sum of its parts: we have taken great care to unify the styles of individual contributors and to structure the contents of the individual chapters. Thus the book brings together, in a timely fashion, a comprehensive view of exciting new developments in utility indifference pricing.
Classical work in the 1980s and 90s concentrated on the development of formulas for pricing and hedging of ever more exotic derivatives. Much of the work assumed complete markets, and the common belief was that it was always possible to choose a pricing kernel, or to choose a specific equivalent martingale measure to compute prices. But the markets are generally incomplete, and it may be impossible to hedge against all sources of randomness. Typical examples of such sources of randomness include stochastic volatilities, random jumps, and nontradable assets. The idea of this book came just as financial mathematicians and engineers started to develop pricing and hedging procedures under more realistic assumptions.
As suggested by the quote "Nothing can have value without being an object of utility" by Karl Marx, we tried to enlist the contributors who have been part of a recent wave of interest in utility-based pricing, into writing a book introducing the subtle intricacies of this nonlinear pricing scheme.
Utility indifference pricing was first introduced in the early nineties by Hodges and Neuberger, but it had to wait almost an entire decade to catch on with financial mathematicians. It was rediscovered by Davis "60,62" and used by Henderson "119" and Musiela and Zariphopoulou "195,196,199", who considered the case of a derivative written on a nontraded asset whose price dynamics are given by a geometric Brownian motion. Most of these contributions are restricted to the case of the exponential utility function. Indeed, in the case of the power utility, one is only able to obtain bounds on the prices. Simultaneously, developments in functional analysis and convex duality associated to the names of Delbaen, El Karoui, Fritelli, and many others brought theoretical tools to the forefront. It was time to bring all these developments together in textbook form. We started our crusade three and a half years ago. We were heartened by the positive responses of the research leaders in this field to our invitation to contribute to the book.