For quite some time there has been a need for a modern treatment of the principles of finance suitable for the beginning Ph.D. graduate student. This rigorous, thoughtfully constructed, and thoroughly excellent text more than fills the bill. The ideas are carefully developed in a discrete time setting with both rigor and intuition – no easy pedagogic task since it requires an uncommonly sensitive balance between the Scylla of sterile formalism and the Charybdis of blowsy chat. The decision to work in a strictly discrete time setting is entirely appropriate for a beginning course and is to be much applauded; the seeming ease of analysis in continuous time comes at the expense of a deeper mathematical foundation that can obscure the underlying economic principles.

The order of development is natural. The text begins with the cornerstone of modern finance, the absence of arbitrage and the implications of this absence for pricing. It moves on to a careful development of risk and utility theory and from there goes naturally into the basic portfolio problem. Spanning and completeness are given a thorough airing and the authors share my view of the importance of this topic, which is seldom treated in the fullness it deserves. When the mean variance analysis and the CAPM are introduced, starting with a very nice tutorial on the Hilbert space approach, the student is ready for it as a special case of the more general development that has preceded.