Choice Review

One of the major changes that Capinski (AGH Univ. of Science and Technology, Poland) and Zastawniak (Univ. of York, UK) made in this second edition (1st ed., 2003) is to start each chapter with the presentation of a case study and to end each chapter with a thorough discussion of that study. The authors also added new material on time-continuous models, along with the essentials of the mathematical arguments. They included complete proofs in the discrete setting of the fundamental theorems of mathematical finance, i.e., those regarding the relationship of arbitrage-free models and the existence of risk-neutral probability vectors. Though the aim is to provide a work appropriate for second- and third-year students, the mathematical prerequisites, which include, at least, courses in multivariate calculus and mathematical probability, along with a smattering of linear algebra, would make that a difficult goal to attain in many US undergraduate curricula. The current book is more substantial than, say, Sheldon Ross's An Elementary Introduction to Mathematical Finance (2nd ed., 2002), but lighter than Douglas Kennedy's Stochastic Financial Models (CH, Aug'10, 47-6915). But, as stated in the first edition, the book is a worthwhile investment because in a single volume "it teaches two Nobel Prize-winning theories." Summing Up: Recommended. Upper-division undergraduates and graduate students. D. Robbins Trinity College (CT)