Book Review. Prices in Financial Markets. Michael U. Dothan

Abstract

This book provides a “unified treatment of selected topics in the theory of financial markets” and an “introduction to the mathematics of this theory.” The selection of topics is roughly the same as in Harrison and Kreps (1979) and Harrison and Pliska (1981). Thus, the focus is on arbitrage, state prices, and complete markets. The mathematics consists of the theory of semimartingales and stochastic calculus. The book will be most useful as a supplementary text for Ph.D. courses on multiperiod financial models. Chapters 1–6 cover the finite-state, discrete-time model. Excluding Chapter 5, which I will describe in a moment, the material is a proper subset of that in Chapters 5, 7, and 8 of Huang and Litzenberger (1988) or Chapters 2, 8, and 10 of Ingersoll (1987). The treatment is very precise and includes many numerical examples. This may be helpful in the first Ph.D. course for covering the basic concepts of arbitrage, linear pricing rules, etc. The book would be more useful in this regard, however, if it made a better connection with the existing finance literature.